Re: AI-GEOSTATS: RES: Tomorrow: Webinar: April 28th, Applied Example of Data Science Technology
Is it just me or does this advert say Monday 28th April??
http://www.kriging.com/whereisshe.htm
From: Marcus Mattos Riether marcus.riet...@caixaseguros.com.br
To: Lisa Solomon li...@salford-systems.com; ai-geostats@jrc.it
ai-geostats@jrc.it
Sent: Tuesday, April 28, 2015 11:43 AM
Subject: AI-GEOSTATS: RES: Tomorrow: Webinar: April 28th, Applied Example of
Data Science Technology
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{margin-bottom:0cm;}#yiv7785629914 ul {margin-bottom:0cm;}#yiv7785629914 Dear
Lisa, I had already filled-up my agenda for today at the time of seminar. I
would be very happy if you could send me a recording. Best regards,
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| | Marcus M Riether
Gerente de Resseguro
Gerência de Resseguro - GERSEG
Diretoria Técnica e de Controle de Riscos - DIRAT
Tel + 55 61 2192 2759 |
De: gregoire.dub...@gmail.com [mailto:gregoire.dub...@gmail.com]Em nome de Lisa
Solomon
Enviada em: segunda-feira, 27 de abril de 2015 16:52
Para: ai-geostats@jrc.it
Assunto: AI-GEOSTATS: Tomorrow: Webinar: April 28th, Applied Example of Data
Science Technology Webinar: Monday, April 28th This webinar will be a
step-by-step presentation that you can repeat on yourown geo, spatial AND
APPLIED datasets!Although the focus is ROI and Business,corresponding GEO and
SpatialApplications include: scenario planning, risk
Re: AI-GEOSTATS: The END of alghalandis.com
Sorry to see you go. Isobel From: Younes Fadakar yfa.st...@ymail.com To: Ask Geostatisticians ai-geostats@jrc.it Cc: alghalan...@ymail.com alghalan...@ymail.com Sent: Wednesday, February 6, 2013 6:48 AM Subject: AI-GEOSTATS: The END of alghalandis.com Dear All, Just to let you know that I don't maintain the web-site (address) http://alghalandis.com anymore! You are more than welcome however to contact me via emails: alghalan...@ymail.com or yfa.st...@ymail.com Best Regards, Younes yfa.st...@ymail.com
AI-GEOSTATS: Re: Backtransforming variance
Hi
Some of my own thoughts on backtransforming the variance go as follows:
the backtransform for the variance in lognormal theory is exp{logarithmic
variance-1} times the square of the mean. In kriging this would adapt to
exp{logarithmic kriging variance-1} times the estimated value squared. Again
you can substitute 10 for exp if you use log10 for all the calculations.
However, this is not useful for producing confidence levels since the lognormal
does not follow the Central Limit Theory and a Normal approximation does not
work in practice.
Better to use lognormal theory such as described on the second page of my
extract. The 'Psi' factors provide multiplicative factors for confidence
levels, i.e. you multiply the Psi factor by the estimated value to get a
confidence.
It really depends why you want to backtransform the variance. For a map,
backtransform the variance, maybe just use exp{kriging variance-1} for a
relative variance. For confidence levels, use the Psi factors.
Hope this helps
Isobel
http://www.kriging.com
AI-GEOSTATS: Re: large dataset and variography...estimation...sim
Younes You can try what we used to do in the bad old days when it took 20 minutes to calculate a semi-variogram on 1,000 samples -- moving windows. Choose a sub-region size which includes about 1,000 samples. Calculate and graph from the samples in this window. Shift half-a-window in one direction. Repeat. Then display all of your graphs as a 'map' for each level. In 1981, I covered the floor of an empty meeting room with computer print out ;-) Thank god for graphics. This approach has the added advantage of being able to visually assess stationarity or lack-of. Only then should you consider modelling. Isobel http://www.kriging.com/shopping/EcoSSe_3D_details.htm + + To post a message to the list, send it to ai-geost...@jrc.ec.europa.eu + To unsubscribe, send email to majordomo@ jrc.ec.europa.eu with no subject and unsubscribe ai-geostats in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
AI-GEOSTATS: Re: Wikipedia geostatistics article
Can I offer a couple of rough attempts from our web collections: http://www.kriging.com/whatiskriging.html is a short description for those coming to geostats cold and http://www.kriging.com/RSMA1978/ is a 500 word article I was persuaded to write for the student magazine at the Royal Scool of Mines 30 years ago. They wanted a simple explanation!! Feel free to use anything you find useful. I did try registering for editing articles on Wikipedia but failed to discover how to make amendments stick!! Good luck and keep us posted. Isobel + + To post a message to the list, send it to ai-geost...@jrc.ec.europa.eu + To unsubscribe, send email to majordomo@ jrc.ec.europa.eu with no subject and unsubscribe ai-geostats in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
AI-GEOSTATS: Re: Sign of the Lagrange Multiplier Used in Back-transform
Yang Yes the lagrangian multipier is subtracted, assuming you used the semi-variogram in your kriging equations. If you use the covariance, it is added. The extra terms in the back transform are to correct for the difference between the variance of the true values and the variance of the estimators. If you are estimating at points, the estimator is a weighted average which will have a smaller variance than single point values. Back transforming values with a smaller variance will bias the estimates downwards. If you want unbiassed estimated values, you have to follow the formula. Hope this helps Isobel http://drisobelclark.kriging.com --- On Mon, 21/12/09, yang yu fareyouw...@gmail.com wrote: From: yang yu fareyouw...@gmail.com Subject: AI-GEOSTATS: Sign of the Lagrange Multiplier Used in Back-transform To: ai-geostats@jrc.it Date: Monday, 21 December, 2009, 21:02 Hello all, I'm trying to apply the lognormal kriging method to a highly negatively skewed dataset (data were reflected first). The back_transform formula given in the reference book takes the following form: Z(x) = EXP[ EstimatedValue + KrigingVariance/s - LagrangeMultiplier] in which the Lagrange multiplier is subtracted from the the first 2 items. Is this formula assuming that the Lagrange multiplier value calculated for each block/cell is POSITIVE? All of the Lagrange values I got for my dataset are NEGATIVE. In this case, should the negative Lagrange values be ADDED to the first 2 items? Many thanks for any guidance and happy hollidays Regards, Yang + + To post a message to the list, send it to ai-geost...@jrc.ec.europa.eu + To unsubscribe, send email to majordomo@ jrc.ec.europa.eu with no subject and unsubscribe ai-geostats in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
AI-GEOSTATS: Re: Unconditional simulation
Nick The simplest way would be to do a aussian simulation and then do a rank transfrom on the results, I think. Isobel http://www.kriging.com --- On Tue, 17/11/09, Nick Hamm n...@hamm.org wrote: From: Nick Hamm n...@hamm.org Subject: AI-GEOSTATS: Unconditional simulation To: r-sig-...@stat.math.ethz.ch, ai-geostats@jrc.it Date: Tuesday, 17 November, 2009, 9:06 Dear all I want to simulate a spatially-correlated random field which follows a uniform rather than than Gaussian distribution. Does anybody know a straight-forward way to do this? Nick + + To post a message to the list, send it to ai-geost...@jrc.ec.europa.eu + To unsubscribe, send email to majordomo@ jrc.ec.europa.eu with no subject and unsubscribe ai-geostats in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/ + + To post a message to the list, send it to ai-geost...@jrc.ec.europa.eu + To unsubscribe, send email to majordomo@ jrc.ec.europa.eu with no subject and unsubscribe ai-geostats in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
AI-GEOSTATS: Re: Straightforward calculation of (cross-) covariogram (covariance function)?
Meng Your question sounds very complicated, so forgive me if I give a simplistic answer. Read our 1987 paper called a novel approach to co-kriging which explains what is now known as the non-co-located cross semi-variogram. You can download a copy from my personal website at: http://drisobelclark.kriging.com/resume/ Follow Publications link. Noel Cressie's book on Statistics for Spatial Data is probably a good definitive reference for co-kriging of both co-located and non-co-located types, although it is heavily mathematical. Computationally, it uses all observations on both variables and is faster than calculating the ordinary semi-variogram on the larger data set. I cannot speak for the software you are using, but that is certainly how ours behaves. You are correct that the sill will be biassed downwards if the overall mean is estimated. However, the bias should be equal to the variance of the error on the estimation of that mean, which should be minimal compared to the variance between individual samples -- even for a small data set. Isobel + + To post a message to the list, send it to ai-geostats@jrc.it + To unsubscribe, send email to majordomo@ jrc.it with no subject and unsubscribe ai-geostats in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
AI-GEOSTATS: Re: 3D Kriging neighborhood size
Greg The answers to your questions depend heavily on what sort of data you have and what software you are using. If you are using borehole or other drilling data, sections of core down a hole will tend to get very similar weights. Most mining packages recommend compositing up into lengths of core equivalent to your block (bench) height. In this way you can effectively use more sampling but still have a reasonably small number of equations to solve. If you are working with other 3D sampling, for example fisheries or meteorological data, which is irregular in 3D then the number of samples is more sensitive. There are many varied attitudes to negative weights, but they are usually the computer's way of telling you to narrow your search ;-) Most software packages have a limitation on the number of equations they can solve and this will reflect the confidence of the programmer in the computer's precision. It really has nothing to do with the kriging as such. We use a maximum of 80, for example. Personally, I do not use samples outside the range of influence unless I am doing Universal Kriging or Kriging with external drift, where they are useful in characterising the trend component. If you have very sparse data, this can lead to strange artifacts as the search sphere moves and single samples drop out and come in. This is not a fault of the kriging, but of the paucity of your data -- a sign you need more samples, in plainer talk! Smoothing these out by increasing your search radius can be misleading since the map looks acceptable when it is actually very unreliable. If you have very dense data, reduce your search radius down from the range of influence. Otherwise you will use a lot of computer time just tracking down the closest samples. Hope this helps and look forward to other viewpoints. Happy New Year! Isobel http://www.kriging.com --- On Wed, 7/1/09, Greg White gregwh...@inbox.com wrote: From: Greg White gregwh...@inbox.com Subject: AI-GEOSTATS: 3D Kriging neighborhood size To: ai-geostats@jrc.it Date: Wednesday, 7 January, 2009, 4:28 PM All, First of all a happy 2009 to everyone! I have a few (beginner?) questions about the neighborhood size (number of points) for Kriging, in particular in 3D: 1) Firstly, I would just like to hear some user experiences - what number have you used in the past? Was that 3D? What range of numbers would you normally test? 2) If I understand correctly, Kriging weights can become negative, but I get the impression that normally the large majority of the weights are positive. Could I therefore assume that if I use 100 points, then the smallest weights are likely to be (much) smaller than 0.01? 3) I understand that (except for simple Kriging), it can be usefull to use a larger search neighborhood than the variogram range. What about the opposite, if you have relatively dense sampling, and there are many points within, say, one tenth of the range? Many thanks, Greg + + To post a message to the list, send it to ai-geostats@jrc.it + To unsubscribe, send email to majordomo@ jrc.it with no subject and unsubscribe ai-geostats in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/ + + To post a message to the list, send it to ai-geostats@jrc.it + To unsubscribe, send email to majordomo@ jrc.it with no subject and unsubscribe ai-geostats in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
AI-GEOSTATS: Re: DDH vs BH
Hi I tackled a similar problem back in the early 80s on a South-African Pb-Zn project where percussion holes had been used to infill a previous diamond drilling campaign. The company allowed me to publish the results. The reference is: Clark, I, 1983: Reserve estimation -- a geostatistical case study on the comparability of drilling methods in Surface Mining and Quarrying, Inst. Min. Metall., London, pp.135- 144 and a copy can be read or downloaded from my personal web page at: http://uk.geocities.com/drisobelclark/resume (follow publications link). I also find a variation of cross validation useful where you use the suspect results as the actual values and the more reliable data set to provide the estimates. This is useful particularly for highlighting bias between the sampling methods. It is discussed in my 1979 APCOM paper Does Geostatistics Work? but I have used it often right up to the present for comparing sampling methods, dates of sampling and so on. Hope this helps Isobel http://www.kriging.com M. Nur Heriawan [EMAIL PROTECTED] wrote: Dear list, I am doing the structural analysis for Pb-Zn grade in 3D. In the first step, I have used the diamond drill hole (DDH exploration) data. Then I work separately using blast hole (BH) data with number of data is much larger than DDH, but BH data cover the area much less wider in 3D space compare to DDH data. I would like to check the spatial consistency of Pb-Zn grade by statistics and variography analysis between DDH and BH. In this case is interesting also to discuss about change of support as the BH data have much closer spacing compare to DDH data, and BH result sludges/cuttings compare to DDH which result cores for assay data. I am performing the analysis for each rocktypes group (domain). I will be happy if anyone here in the list could share or suggest me any references related to this subject. Thank you for kind help and attention. Regards, --- M. Nur Heriawan Earth Resources Exploration Research Group Faculty of Mining and Petroleum Engineering Institut Teknologi Bandung (ITB) Jl. Ganesha 10 Bandung 40132 INDONESIA http://www.mining.itb.ac.id/heriawan + + To post a message to the list, send it to ai-geostats@jrc.it + To unsubscribe, send email to majordomo@ jrc.it with no subject and unsubscribe ai-geostats in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
AI-GEOSTATS: Re: coordinates units and semivariogram calculation
Pedro Why don't you work with the original co-ordinates? X in cm Y in metres. So long as you do not expect the semi-variogram to be isotropic, it does not matter what units you use. So long as you know, the computer does not need to! Isobel http://www.kriging.com Pedro Mardones [EMAIL PROTECTED] wrote: Dear list members; I would like to have any opinion (or suggestion) about the following situation. I have a collection of data points spatially arranged on a 12 by 11 grid where the horizontal axis was measured in cm at 1 cm intervals (from 1 to 12 cm) and the vertical axis was measured in meters at 1.5 m intervals (from 1.5 to 16.5 m). The data set doesn't represent a portion of land but instead they are points within a (wood) pole that were assessed for some physical properties. That's the reason of such dissimilar coordinates units. I would like to create a map using these measured locations by interpolating the information of interest on a set of non-observed points within the grid. I tried by expressing all the values in cm or m, but that didn't work well. For example, if I express everything in cm, the max distance on the vertical direction is of course much bigger than the max dist observed on the x-axis. I'm wondering what could be the best way to approach the problem when I have such a different scales on the coordinates. Is it possible to express the coordinates in a relative scale (0-1) instead of Cartesian coordinates and then perform the analysis to obtain the variograms by having a relative measure of h instead an absolute one? Thanks in advance and sorry for cross postings PM + + To post a message to the list, send it to ai-geostats@jrc.it + To unsubscribe, send email to majordomo@ jrc.it with no subject and unsubscribe ai-geostats in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
AI-GEOSTATS: Re: Adjusted ANOVA and power model, SAS PROC Mixed
Tomas This is probably the model also known as the generalised linear: gamma(h)=nugget effect + slope x distance-to-a-power parameters are slope and power for distance. I may be wrong!! Isobel http://www.kriging.com tomas hlasny [EMAIL PROTECTED] wrote: Dear all, I am calculating ANOVA adjusted for spatial autocorrelation using SAS Proc Mixed. It uses variogram to reduce the number of degrees of freedom. Can somebody help me, how to define a power model? Normaly, the parameters are sill, range (resp. scale), exponent and nugget respectively. However, as I found in SAS manual that power models is defined only using 2 params. Can somebody help? Thank`s a lot Best regards Tomas Dr. Tomá Hlásny NATIONAL FOREST CENTRE Department of Ecology and Biodiversity of Forest Ecosystems -- T. G. Masaryka st. 22, SK-96092 Zvolen Slovak Republic http://www.nlcsk.org/ phone: +421/45/532 03 16 fax: +421/45/531 41 92 NARODNE LESNICKE CENTRUM http://www.nlcsk.org begin:vcard fn:Tomas Hlasny n:Hlasny;Tomas org:National Forest Centre - Forest Research Institute;Ecology and Biodiversity of Forest Ecosystems adr:;;T. G. Masaryka 22;Zvolen;;96001;Slovakia email;internet:[EMAIL PROTECTED] title:Dr. x-mozilla-html:FALSE url:www.nlcsk.org version:2.1 end:vcard
AI-GEOSTATS: Re: Help with variogram
Fernando Thank you for your email. I do not know much about variowin and am not up to speed on semi-variograms in Surfer so I am posting your query on the ai-geostats site. I am sure that some of our members can help you out. Email me again if you get no help ;-) Isobel http://www.kriging.com Fernando Cruz [EMAIL PROTECTED] wrote: Hello, I'm a miner engineering student from University of Porto, I was wondering if you could help me with a work I have to do. I'm a starter in Geostatistic, and I'm having some problems in finding a relation between data from surface sismic and from shaft sismic. The thing is that I've some oil research data do you think you can send me a methodology to use surfer or variowin and to find some kind of relation between these to data files. I've from shaft data (check shots) the x,y and z coordinates and I've info about TWT, Average speed through horizonte. I've from surface data (VSP) the TWT and average speed through horizonte. I've info about the six horizonts. So, let me thank you in advance and forgive me for asking these things but I'm really needing some kind of help. Best regards Fernando Cruz
AI-GEOSTATS: Re: Numerical method to solve kriging equations
Adrian It is a common misconception that using the covariance (total sill - semi-variogram) rather than the semi-variogram brings more robust solutions. You get exactly the same answer either way since one is just a constant minus the other. You can avoid solution problems by simple pivoting or by putting the condition equation first -- sum of weights equals 1. If you look at the details of the solution, you generally only have to pivot the first equation to remove the diagonal zeroes. Isobel http://courses.kriging.com Adrian Martínez Vargas [EMAIL PROTECTED] wrote: What about to produce pseudo covariance to replace kriging matrix in term of variogram to make more efficient the numerical solution of the system? The ceros in the matrix diagonal are a problem in robustness and efficiency! Some one knows how to implement something like that? Papers/books can be useful! - Original Message - From: Adrian Martínez Vargas To: ai-geostats@jrc.it Sent: Friday, March 28, 2008 5:23 PM Subject: Numerical method to solve kriging equations Hello dear list What numerical method give faster and robust solution to kriging equations. What to us as C++ library (for example TNT and JAMA?). It is usual to use cholesky in the case of simple kriging. I will appreciate your advice and experiences. Best regards Dr. Adrian Martínez Vargas Revista Minería y Geología ISMM, Las Coloradas, s/n Moa, Holguín, Cuba CP. 83329 http://www.ismm.edu.cu/revistamg/index.htm
Re: AI-GEOSTATS: kriging or IDW in case study of hydrology?
Andrea In theory kriging will honour the sample values provided your semi-variogram model takes the value zero at zero distance. Whether the data are honoured or not depends on which computer package you use and what it does with the semi-variogram at zero. You can force this behaviour by replacing any nugget effect with a short range model component. For example a spherical component with a range of influence of 10cm or some such. See our completely free and public domain kriging game, for how the kriging system works. By the way, IDW will only honour your sample values if the algorithms are written with the same criterion. Isobel http://www.kriging.com Andrea Peruzzi [EMAIL PROTECTED] wrote: Dear list, I'm graduate student in hydrogeology, I've to spatialize data of reservoir thickness, and I need to achieve a map having exactly the sampled value in the sampled localization (piezometers). I've little experience in geostatatistics. I had a look at kriging algorithms, but I did understand that kriging does not preserve the sampled value at sampled locations but it tends to smooth results, even if estimates correctly the unsampled space. So I wonder why should I use Kriging instead IDW (which it should preserve my sampled values): kriging respects the spatial variability but do not respect data As I told you before, I've very small knowledge in geostatistics stuff, but I'm interesting in kriging. Could anyone help me? Thanks a lot, Andrea Peruzzi PS: I apologize for writing you again but it's the first time I'm writing you, then I'm not sure how the mailing list works. Thanks :-) + + To post a message to the list, send it to ai-geostats@jrc.it + To unsubscribe, send email to majordomo@ jrc.it with no subject and unsubscribe ai-geostats in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
AI-GEOSTATS: Re: Correlation between kriging residuals and input data
Gregoire The correlation between actual value and error of estimation is always present to some extent and is simply due to the estimation process. High values will b eunderestimated from neighbouring samples. Low values will be overestimated from neighbouring samples. The only way you can remove this is by using a more complex estimator than a weighted average. Have you plotted the actual value versus the estimates? This will tell you whether you are getting any meaningful prediction or not. Generally, the stronger the correlation here the less you'll get with the errors. FYI: we use (actual - estimate) in our discussions. Not sure why, just a personal preference. Isobel http://www.kriging.com Monica Palaseanu-Lovejoy [EMAIL PROTECTED] wrote: Hi, If there is a very high nugget effect i would expect that the predictions are very close to the mean of the data, with very little variation. In this case you would get a very high correlation (either close to 1 or -1 - depending on how you calculated the residuals). Did you check for local outliers??? If you have a high percentage of local outliers kriging is not a good choice - in my experience - stationarity is usually violated, and the predictions are very poor indeed. Maybe you should investigate other methods of interpolations . one of my favorite is multiquadric radial basis function which in many cases can be compared with kriging, performs better when a high percentage of local outliers exist, and does not require stationarity. Monica Monica Palaseanu-Lovejoy, PhD Jacobs Technology US Geological Survey Florida Integrated Science Center 600 4th Street South St. Petersburg, FL 33701 Ph: 727-803-8747 x 3068 Fx: 727-803-2031 email: [EMAIL PROTECTED] Gregoire Dubois [EMAIL PROTECTED] Sent by: [EMAIL PROTECTED] 01/30/2008 06:59 AM Please respond to Gregoire Dubois [EMAIL PROTECTED] To ai-geostats@jrc.it cc Subject AI-GEOSTATS: Correlation between kriging residuals and input data Dear list, Having fit a variogram to a dataset (indoor radon measurements) and applied cross-validations, I noticed the perfect negative correlation (-0.95) between my kriging residuals and my input data. This means that I am overestimating as much the low values as I am underestimating the high values, something I am expecting since the mean of the residuals - 0, a property of kriging. Fine so far. What I am puzzled about is of the possible reasons of getting such a strong slope (close to -1) of the plot of my residuals against my input data? This, I understand, highlights that I am doing a systematic error somewhere which I want to avoid obviously. I thought I extracted properly the spatially correlated component of my dataset (the variogram of my residuals seems to show a pure nugget effect) but I still can't find any reasonable explanation for the systematic errors. Any hints? I must have missed something obvious here. Many thanks for any feedback. Best regards, Gregoire
Re: AI-GEOSTATS: Variogram
Jamina Different software packages have different requirements for defining anisotropy. Some will allow you to define completely a model for each major axis of the anisotropy ellipse. The simplest (geometric anisotropy) just accept anisotropy 'factors' for the range of influence. In my experience, zonal anisotropy usually indicates geological non-homogeneity and/or discontinuities. For example, you may have a fult line which increases the apparent sill when you cross it. Or you may have different geological zones, again increasing the sill when you cross from one to the other. Isobel http://www.kriging.com Jamina Dogic [EMAIL PROTECTED] wrote: Dear experts, I¢ll be very grateful if you can help me with following question. I am geologist, and I need to use variogram for ore estimation process. I have problem with managing data in variography. I am looking at variation of cooper content in porphyry type of deposit and I did variograms in 4 directions. 0, 45, 90 and 135 degrees. I have both geometric and zonal anisotropy. My question is connected with final variogram model, does it means that I need to produce only one model of variogram which will be suitable for all 4 directions, some kind of average variogram model for all direction. Thanks in advance Jasmina Beljic Belgrade, Serbia - Never miss a thing. Make Yahoo your homepage. - Never miss a thing. Make Yahoo your homepage.
Re: AI-GEOSTATS: Variogram
The general method is to try to apply the same sort of shape in each direction, changing the range of influence for the different directions. Have you tried looking at semi-variogram maps. These can often help with anisotropy when individual directional semi-variograms are vague. Isobel enayat khojasteh [EMAIL PROTECTED] wrote: Dear Mrs. Clark, As you have mentioned,anisotropy is an important aspect in modeling. For me one question always,is: although,we have usually rather strong structures in vertical direction, the horizontal direction is very much vague and with changing every graphical parameters or search parameters,it is changed very much. 1-If every change in such parameters affect our models how can we trust them? 2- Is there any possibility to make a link between vertical and horizontal variograms ( so that we may improve,the horizontal variogram,with the help of vertical variogram)? I would appreciate to have your idea about it. Kind Regards E. R. Khojasteh Isobel Clark [EMAIL PROTECTED] wrote:Jamina Different software packages have different requirements for defining anisotropy. Some will allow you to define completely a model for each major axis of the anisotropy ellipse. The simplest (geometric anisotropy) just accept anisotropy 'factors' for the range of influence. In my experience, zonal anisotropy usually indicates geological non-homogeneity and/or discontinuities. For example, you may have a fult line which increases the apparent sill when you cross it. Or you may have different geological zones, again increasing the sill when you cross from one to the other. Isobel http://www.kriging.com Jamina Dogic [EMAIL PROTECTED] wrote: Dear experts, I¢ll be very grateful if you can help me with following question. I am geologist, and I need to use variogram for ore estimation process. I have problem with managing data in variography. I am looking at variation of cooper content in porphyry type of deposit and I did variograms in 4 directions. 0, 45, 90 and 135 degrees. I have both geometric and zonal anisotropy. My question is connected with final variogram model, does it means that I need to produce only one model of variogram which will be suitable for all 4 directions, some kind of average variogram model for all direction. Thanks in advance Jasmina Beljic Belgrade, Serbia - Never miss a thing. Make Yahoo your homepage. - Never miss a thing. Make Yahoo your homepage. - Never miss a thing. Make Yahoo your homepage.
Re: AI-GEOSTATS: New geostatistical open source software
Why, thank you, Adrian. I like to strike a happy balance between sticking with what I know and being open to new ideas ;-) If it is good enough for NASA. Isobel Adrián Martínez Vargas [EMAIL PROTECTED] wrote: Isobel Clark I apologise about Fortran
Re: AI-GEOSTATS: New geostatistical open source software
Hi Michael Nice to see someone comfortable with rambling. I think we should have more of that in the list! Being an old warhorse and too far gone to change, I still use Fortran. My excuse is always if it's good enough for NASA.. Visual Basic is pretty good too but Fortran is still the faster 'computational' language and a very easy interface. I guess we'll just have to phase out as the compilers disappear ;-) Isobel http://www.kriging.com
AI-GEOSTATS: Re: Kriging variance, lagrangian multiplier
Hi Abani You need my 1983 Mathematical Geology paper, Regression Revisited which can be downloaded by folloing the publications link at http://uk.geocities.com/drisobelclark/resume Or, with less math, A simple alternative to Disjunctive Kriging written with Flemming Clausen in 1981 (TransIMM). Also on the web. I have seen later papers which propose similar with a lot more mathematics. Hope this helps Isobel Abani R Samal [EMAIL PROTECTED] wrote: My First question: I am using a mining software to get a krigged block model. The tool also saves a parameter called Slope of Regression. The Slope of Regression is defined as (Block Variance Kriging Variance +Lagrange_multiplier)/(Block_variance-KrigingVariance+2*abs(Lagrange_Multiplier)) provided the denominator is not zero. Unfortunately, there is NO literature available (Including no help file). I have hard time to understand what this Slope of Regressionmeans and how this slope is usable. I'll highly appreciate your thought on this. My second question: If s is the sample, v is the block and V is the whole panel of blocks or the whole deposit, the Kriges additive relation can be written as: ó 2 (s,V) = ó2(s,v) + ó2(v,V) But how is: ó2(s,V) related to ó2ok? (ó2okKriging variance), under what condition? Abani R Samal Lakewood, CO __ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com
Re: AI-GEOSTATS: modelling and goodness of fit
Andrea We use Cressie's goodness of fit statistic which allows for number of pairs and other factors in semi-veriogram fitting. You can find a paper of his in Methematical Geology around 1992, or in his book. It is also illustrated in our free tutorial material at www.kriging.com Isobel Andrea Sciarretta [EMAIL PROTECTED] wrote: Hi, Im working on variogram modelling and in the majority of cases only R2 is available to evaluate the best-fit values, but in cases of non-linear functions, it is very criticized. Are there other standard methods to evaluate the goodness of a fit of a non-linear function (for example asymptotic confidence intervals) and how to calculate them, considering that the majority of geostatistical software do not perform any alternative coefficient? Thank you Andrea
Re: AI-GEOSTATS: Intrinsic Random Functions -- what it mean for lambda to annihilate a polynomial?
Olumide I would think what they mean is that each order of polynomial has to be balanced between the 'drift' at the actual estimated point and the weighted average of the samples which proovides the estimator. For this you have to introduce an extra lamda and an extra equation on the kriging system which guarantees the unbiassedness of the estimate. At least, that is what happens in Universal Kriging. What is annihilated is any possible bias due to the order k. I do not know why lamda is referred to as a discrete measure. Isobel http://www.kriging.com/courses Olumide [EMAIL PROTECTED] wrote: Hello - I've made some progress understanding what intrinsic random functions are, and what increments are in that regard. The next question that's still puzzling me is the question of what the discrete measure lambda and the annihilation of polynomials. Quote from Geostatistics Modeling Uncertainty by Chiles and Delfiner page 238: Definition: a discrete measure lambda is allowable at the order k if it annihilates polynomials of degree less than or equal to k Questions: 1. what does it mean for lambda to annihilate a polynomial 2. why the need to annihilate those poor polynomials (what have they done wrong? ;-) ) Thanks, - Olumide + + To post a message to the list, send it to ai-geostats@jrc.it + To unsubscribe, send email to majordomo@ jrc.it with no subject and unsubscribe ai-geostats in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
Re: AI-GEOSTATS: Intrinsic Random Functions -- what it mean for lambda to annihilate a polynomial?
Olumide I recommend you work through our free tutorial on kriging with trend. It discusses Universal Kriging rather the IRF-K but I think it will answer your question better than I can do in a short email. Yes you can annihilate the trend by making the weighted average of the trend equal zero but it makes more sense to make the trend from the samples honour the trend at the point being estimated. Isobel http://www.kriging.com Olumide [EMAIL PROTECTED] wrote: Isobel Clark wrote: I would think what they mean is that each order of polynomial has to be balanced between the 'drift' at the actual estimated point and the weighted average of the samples which proovides the estimator. For this you have to introduce an extra lamda and an extra equation on the kriging system which guarantees the unbiassedness of the estimate. Sorry but I don't understand what you mean by this. I've been doing some more thinking and reading and here's my GUESS -- please correct me if I'm wrong: Suppose a RF Z(x) can be modeled as: Z(x) = m(x) + Y(x) where m(x) is the drift which is modeled as weighted sum of polynomials of order up to k (e.g. if k = 2, drift is w[0] + w[1].x + w[2].y + w[3].xy + w[4].x² + w[5].y²) and Y(x) a fluctuation or residual about this drift. Removing this drift would require somehow finding values for the weights such that the weighted sum *somehow* becomes zero thus annihilating the *effect* of the polynomials. ???
Re: AI-GEOSTATS: Universal Cokriging -- algebraic dependence between drifts
Hi Olumide You will find the basic kriging system for Multi-variable Universal Co-kriging in our definitive 1987 paper which can be viewed or downloaded from the web at: http://www.kriging.com/publications/Battelle1987 Our thought was that interdependent trends would be adequately handled by including both trends in the co-kriging system. Isobel Olumide [EMAIL PROTECTED] wrote: Hi - On page 312 of Geostatistics: modeling spatial uncertainty the authors Chiles and Delfiner discuss algebraic dependence between drift coefficients of a primary and secondary variable, in the simplest case. Under what typical conditions can such an assumption about drifts be made? In the case of terrain data for example, where the height is the primary variable and the slope or gradient the secondary variable. Are the drift coefficients of both variables ... erm ... dependent? And why. Ultimately, I'm trying to work out the cokriging equation for such a problem. Thanks, - Olumide + + To post a message to the list, send it to ai-geostats@jrc.it + To unsubscribe, send email to majordomo@ jrc.it with no subject and unsubscribe ai-geostats in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
AI-GEOSTATS: Re: What does Drift mean?
Hi You will find drift also referred to as trend, generally understood as a change in the 'expected' value from place to place within your study area. For example, an airborne pollutant with a single source will show higher values close to the source tending to 'thin out' as the distance to the source increases. In this case, the relationship does not just depend on the distance between samples but also on the actual location relative to the source. We have a free tutorial on kriging with trend which can be found by following links on http://www.kriging.com Isobel Olumide [EMAIL PROTECTED] wrote: Hello - I'm still new to geostatistics, and I've come across the term, drift a few times, but I don't really understand what it means. Can someone offer a simple explanation? Thanks, - Olumide + + To post a message to the list, send it to ai-geostats@jrc.it + To unsubscribe, send email to majordomo@ jrc.it with no subject and unsubscribe ai-geostats in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
AI-GEOSTATS: Re: ore grade and reserve estimation
The ones I have are: Applied Mineral Inventory Estimation by Alastair J. Sinclair and Garston H. Blackwell and Case Histories and Methods in Mineral Resource Evaluation (Geological Society Special Publication) by Alwyne E. Annels (Hardcover - Jun 1992) If you surf amazon you should get views and publisher details. Isobel http://www.kriging.com M. Nur Heriawan [EMAIL PROTECTED] wrote: Dear list, I am looking for some books about integrated reserve estimation and grade control (for mine planning). These books are for teaching purpose. From googling, I found two titles: - Ore Reserve Estimation and Strategic Mine Planning: Stochastic Models and Optimizations with Case Studies Dimitrakopoulos, Roussos Springer, 2006 Ore Reserve Estimation and Grade Control J.E. Gill The Canadian Institute of Mining and Met, 1968 - I did not find any reviews about these books. Therefore, before I order them, may somebody give the comment or suggestion. Thank you for kind attention, Regards, --- M. Nur Heriawan Laboratory of Applied Geoscience and Technology Graduate School of Science and Technology Kumamoto University, JAPAN http://www.civil.kumamoto-u.ac.jp/tansa __ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com + + To post a message to the list, send it to ai-geostats@jrc.it + To unsubscribe, send email to majordomo@ jrc.it with no subject and unsubscribe ai-geostats in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
AI-GEOSTATS: Re: Sichel's t estimator
Peter Sorry, that couple of days turned into five weeks! I have put the addenda to the lognormal paper up as images at: http://www.kriging.com/publications/SAIMM_87_addenda.htm The one you are interested in is probably Addendum 2, with Sichel's maximum likelihood theory. I will put a proper link on the publications page when I get time. If you have any queries, come back to me. All the best Isobel Peter Bossew wrote: Thanks Isobel for the very fast reply. There is no hurry... I am just curious because I never heard about Sichel's t before. Anyhow, my impression is that altogether the lognormal distribution is less trivial a thing than it may appear at first glance. (I am currently working on a paper about automatic identification of extrema / spatially: hot spots, by exploiting the differences of estimating the lognorm parameters from the data and from the moments, respectively.) Peter Isobel Clark writes: Hi Peter Sorry about the addendum. You are quite correct, none of the addenda seem to have made it onto the web page!
AI-GEOSTATS: RE: spatial weights
Yes, but the problem with averaging the data in the cell is that the average
has a different standard deviation, depending on the layout of the sampling
within each cell.
So, if you decluster by averaging each cell you can end up with a set of
cells which all come from different distributions -- same mean but different
variance. Not stationary at all! Better to select one sample from each cell.
Isobel
http://www.kriging.com
Digby Millikan [EMAIL PROTECTED] wrote:
v\:* {behavior:url(#default#VML);} o\:* {behavior:url(#default#VML);}
w\:* {behavior:url(#default#VML);} .shape {behavior:url(#default#VML);}
You have to uncluster the data e.g. in resource exploration programs
often more sampling takes place
in the higher grade zones, so this has to be compensated for by using an
equal amount of sample
data from each area. If two samples are taken at one location it makes sense
to average them, and
if the data is normally distributed and stationariay the data within each
cell is normally distributed
so the average of that cell, is the mean of the data within it?
-
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Bill Thayer
Sent: Saturday, 17 February 2007 7:29 AM
To: ai-geostats@jrc.it
Subject: AI-GEOSTATS: spatial weights
In Isaaks and Srivastavas Applied Geostatistics (1989), the use of
de-clustering weights are described as a method for computing estimates of
the mean and variance with data that are clustered geographically.
I would appreciate feedback regarding the theoretical basis for using spatial
weights to compute estimates of the mean and (population) variance, and for
making inferences regarding population parameters. Through simulation tests, I
have some evidence that this method performs fairly well with weights derived
from Thiessen polygons for populations with varying degrees of spatial
autocorrelation and skewness. However, I am not aware of any theoretical
basis/justification for the weights. Intuitively, the use of spatial weights
to account for geographic location of the observations (and possibly spatial
autocorrelation among the observations) seems analogous to the common practice
in survey statistics of adjusting sample weights to correct for non-response,
etc, where the objective is to adjust the weights to account for observed
differences between some attribute of the observations (e.g., socioeconomic
status) and the target population. In the spatial weighting case,
the adjustment is to correct for observed geographical clustering. One
notable difference is that in many cases, the data that I work with was not
collected using random sampling methods.
Your feedback would be appreciated.
Best regards,
Bill
Re: AI-GEOSTATS: Sichel's t estimator
The later papers discuss the variations on the lognormal prompted by Sichel's revivavl of interest in the late 1980s. The actual lognormal basis is not discussed in those papers. I am tracking down a copy of my original paper to add the mathematical addenda on the 1987 paper and will post to the list when it is available. Isobel http://www/kriging.com Eric PIRARD [EMAIL PROTECTED] wrote: Hi Peter, Additional work has been done by Sichel and Kleingeld more recently. They should be more available than the original one : Comparative study of three frequency-distribution models for use in ore evaluation Sichel, H S; Kleingeld, W J; Assibey-Bonsu, W J S Afr Inst Min Metall V92, N4, April 1992, P9199 New generalized model of observed ore value distributions H. S. Sichel, C. E. Dohm 8c W. J. Kleingeld, Transactions - InsXitution of Mining Metallurgy, Section A, 104(May- Aug), 1995, pp AllS-A123 New generalized model of observed ore value distributions Sichel, H.S. / Dohm, C.E. / Kleingeld, W.J., International Journal of Rock Mechanics and Mining Sciences Geomechanics Abstracts, Jan 1996 Eric PIRARD /. UNIVERSITE DE LIEGE (ULg) ArGEnCo Dpt GEMME - Georesources Mineral Imaging Sart Tilman B52 4000 Liège (Belgium) Tél. : +32-4-3669528Fax.: +32-4-3669520 http://www.mica.ulg.ac.be + + To post a message to the list, send it to ai-geostats@jrc.it + To unsubscribe, send email to majordomo@ jrc.it with no subject and unsubscribe ai-geostats in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
AI-GEOSTATS: Re: Kriging using Nugget Model
Mehari SURFER will be giving you the arithmetic mean of the samples which fall inside your search radius, not all possible samples. Effectively, you are getting a moving average. Isobel http://www.kriging.com
AI-GEOSTATS: Re: Kriging using Nugget Model
Mehari If you use a semi-variogram which is just nugget, the kriging estimate will be the arithmetic mean of the sample values and the standard error will be the standard sigma/root n of classical statistics. Isobel Mehari Tekeste [EMAIL PROTECTED] wrote: Can I get some suggestion on this issue? How good is estimation using kriging system that uses a nugget model? I have a geodata and the semi-variogram was best fit using a nugget model (with semi-variance=C_0; where C_o is a nugget for all h (lag distance) values. Thanks. Mehari Z. Tekeste, Ph.D. Research Scientist Department of Agriculture Western Kentucky University 1906 College Heights Blvd. #41066 Bowling Green, KY 42101-1066 Phone: 270-745-5972 Fax: 270 745 5972 And God said, Let us make man in our image, after our likeness: and let them have authority over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepeth upon the earth. Genesis 1: 26. + + To post a message to the list, send it to ai-geostats@jrc.it + To unsubscribe, send email to majordomo@ jrc.it with no subject and unsubscribe ai-geostats in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
AI-GEOSTATS: Re: Lagrange Multiplier
NjeriThe full _expression_ for the estimation variance conains three terms:1) twice the weighted average of the semi-variograms between each sample and the point to be estimated2) the doubly weighted average of all the semi-variograms between every possible pair of samples used in the estimation3) if estimating over an area or volume, the average semi-variogram between every pair of points inside that area or volume(2) and (3) can also be described as the "variance amongst the sample values" and the "within-block variance" respectively and are subtracted from (1). When ordinary kriging is derived the lagrangian multiplier is introduced to make sure the weights add up to 1. It turns out that the lagrangian multiplier is equal to half of term (1) minus term (2). Intuitively, it is the balance between how well your samples relate to the unknown value and how well they relate to one another.For example: if your samples are all close to the estimated location, term (1) will be small; if they are all close to one another term (2) will be small. Ideally we want term (1) to be as small as possible and term (2) to be as big as possible. This translates into: "lagrangian multiplier value big and positive" samples are either too far from point to be estimated or are highly clustered. "lagrangian multiplier big and negative" samples (too?) close to estimated point and widely spaced around it. One might see a zero lagrangian multiplier as the perfect balance between the sampling layout and the prediction of unknown values. Or not, as you prefer.Hope this helps Isobel http://www.kriging.comNjeri Wabiri [EMAIL PROTECTED] wrote: Dear listJust a newbabie questionWhat is the statistical interpretation of the Lagrange multiplier in kriging.At least I know if its positive we have a high kriging variance and vice versa.Grateful for a response and a referenceNjeri ++ To post a message to the list, send it to ai-geostats@jrc.it+ To unsubscribe, send email to majordomo@ jrc.it with no subject and "unsubscribe ai-geostats" in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list+ As a general service to list users, please remember to post a summary of any useful responses to your questions.+ Support to the forum can be found at http://www.ai-geostats.org/
AI-GEOSTATS: RE: pseudo cross variogram: h=0
PeijunI presume by the "pseudo" cross semi-variogram, you mean the 'non co-located' cross semi-variogram as opposed to the more traditional co-located cross semi-variogram?If so, the difference between the sill of your model and the nugget effect at zero is simply the classical covariance between your two variables. This is one way to calculate the covariance or correlation when you do not have co-located data for a more traditional statical calculation.Interestingly, this cross semi-variogram is the only one which actually takes a non-zero value at zero distance!Personally, I dislike the term "pseudo" which suggests that this is some sort of approximation to the "real" thing. Both approaches to co-kriging have strengths and weaknesses. So long as you are aware of these, you can gain valuable insight into your cross-relationships. Isobel http://www.kriging.comPeijun Li [EMAIL PROTECTED] wrote: Dear Dr. Goovaerts,Thanks for reply.I compute the pseudo cross variogram from bi-temporal images for changedetection. I found that when lag h=0, the pseudo cross variogram imageobtained highlights the change in the image. So, I would like to understandwhy it happens.PeijunPeijun LiInstitute of Remote Sensing and GISPeking University, Beijing 100871P R China _ From: Pierre Goovaerts [mailto:[EMAIL PROTECTED] Sent: Thursday, September 21, 2006 2:15 AMTo: Peijun Li; ai-geostats@jrc.itSubject: RE: AI-GEOSTATS: pseudo cross variogram: h=0Hi,It just represents half the average squared difference between the values ofthe two variablesmeasured at the same location.. I don't know why you compute the pseudocross-variogrambut, personally, I don't like this statistic, mainly because of the lack ofinterpretation... for example, it cannot take negative values, hence you can't differentiatebetween positive and negative correlations. It is useful mainly when the twovariables have not been measured at the same locations.Pierre Pierre GoovaertsChief Scientist at BioMedware Inc.Courtesy Associate Professor, University of FloridaPresident of PGeostat LLCOffice address: 516 North State StreetAnn Arbor, MI 48104Voice: (734) 913-1098 (ext. 8)Fax: (734) 913-2201 http://home.comcast.net/~goovaerts/ _ From: [EMAIL PROTECTED] on behalf of Peijun LiSent: Wed 9/20/2006 12:35 PMTo: ai-geostats@jrc.itSubject: AI-GEOSTATS: pseudo cross variogram: h=0Dear List,I recently use the pseudo cross variogram (PCV) for remote sensingapplications. However, I don't know what does the PCV reflect when lag h=0?As we know, when lag h=0, the (univariate) variogram reflects the nuggeteffect. Is there any similar meaning for PCV? Could you give me somereferences related to PCV?Thanks in advance for reply.Peijun LiPeking University
AI-GEOSTATS: Re: Linear regression
DigbyThe variance of the residuals (whether regression or kriging) is the sum of the squared residuals divided by the degrees of freedom. Since the "degrees of freedom" is a fixed number, minimising the variance is identical to minimising the sum of squared residuals.IsobelDigby Millikan [EMAIL PROTECTED] wrote:Is minimizing the sum of the square of the the residuals equal to the minimization of the variance of the residuals? Can we get any intuitive meaning from the relationship between the sum of the squares and the variance?
AI-GEOSTATS: RE: pseudo cross variogram: h=0
PierreIf the relationship between your two variables is negative, the "pseudo" cross semi-variogram will start high and drop off, just like the co-located one. Difference is, the former doesn't go negative, the latter starts at zero and is all negative.One other feature of the "pseudo" version is that it can (if desired) preserve the 'sense' as well as relative direction, providing an 'odd' function rather than the symmetric-around-zero co-located semi-variogram. This can be useful if you are working in space-time or with a phenomenon in which absolute direction is a factor.IsobelPierre Goovaerts [EMAIL PROTECTED] wrote: Hi,It just represents half the average squared difference between the values of the two variablesmeasured at the same location.. I don't know why you compute the pseudo cross-variogrambut, personally, I don't like this statistic, mainly because of the lack of interpretation... for example, it cannot take negative values, hence you can't differentiatebetween positive and negative correlations. It is useful mainly when the two variables have not been measured at the same locations.Pierre Pierre GoovaertsChief Scientist at BioMedware Inc.Courtesy Associate Professor, University of FloridaPresident of PGeostat LLCOffice address: 516 North State StreetAnn Arbor, MI 48104Voice: (734) 913-1098 (ext. 8)Fax: (734) 913-2201 http://home.comcast.net/~goovaerts/ From: [EMAIL PROTECTED] on behalf of Peijun LiSent: Wed 9/20/2006 12:35 PMTo: ai-geostats@jrc.itSubject: AI-GEOSTATS: pseudo cross variogram: h=0Dear List,I recently use the pseudo cross variogram (PCV) for remote sensing applications. However, I don't know what does the PCV reflect when lag h=0? As we know, when lag h=0, the (univariate) variogram reflects the nugget effect. Is there any similar meaning for PCV? Could you give me some references related to PCV?Thanks in advance for reply.Peijun LiPeking University++ To post a message to the list, send it to ai-geostats@jrc.it+ To unsubscribe, send email to majordomo@ jrc.it with no subject and "unsubscribe ai-geostats" in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list+ As a general service to list users, please remember to post a summary of any useful responses to your questions.+ Support to the forum can be found at http://www.ai-geostats.org/
AI-GEOSTATS: Re: pseudo cross variogram: h=0
PeijunThat is interesting to hear. I wish you luck in its use. If you are writing any reports, you may wish to refer to our original paper "A novel approach to co-kriging" published in the 1980s and downloadable from my personal site at http://uk.geocities.com/drisobelclark/resume (follow publications link).IsobelPeijun Li [EMAIL PROTECTED] wrote: Dear Dr. Clark, Thank you for reply. You know that any point (i.e. pixel) in an image has a value (graylevel value), which is different from sparsely sampling data in geosciences. We use the pseudo cross variogram to characterize the spatial cross correlation between two variables.Peijun From: Isobel Clark [mailto:[EMAIL PROTECTED] Sent: Thursday, September 21, 2006 10:28 PMTo: Peijun LiCc: ai-geostats@jrc.itSubject: RE: pseudo cross variogram: h=0 PeijunI presume by the "pseudo" cross semi-variogram, you mean the 'non co-located' cross semi-variogram as opposed to the more traditional co-located cross semi-variogram?If so, the difference between the sill of your model and the nugget effect at zero is simply the classical covariance between your two variables. This is one way to calculate the covariance or correlation when you do not have co-located data for a more traditional statical calculation.Interestingly, this cross semi-variogram is the only one which actually takes a non-zero value at zero distance!Personally, I dislike the term "pseudo" which suggests that this is some sort of approximation to the "real" thing. Both approaches to co-kriging have strengths and weaknesses. So long as you are aware of these, you can gain valuable insight into your cross-relationships.Isobelhttp://www.kriging.comPeijun Li [EMAIL PROTECTED] wrote:Dear Dr. Goovaerts,Thanks for reply.I compute the pseudo cross variogram from bi-temporal images for changedetection. I found that when lag h=0, the pseudo cross variogram imageobtained highlights the change in the image. So, I would like to understandwhy it happens.PeijunPeijun LiInstitute of Remote Sensing and GISPeking University, Beijing 100871P R China _ From: Pierre Goovaerts [mailto:[EMAIL PROTECTED] Sent: Thursday, September 21, 2006 2:15 AMTo: Peijun Li; ai-geostats@jrc.itSubject: RE: AI-GEOSTATS: pseudo cross variogram: h=0Hi,It just represents half the average squared difference between the values ofthe two variablesmeasured at the same location.. I don't know why you compute the pseudocross-variogrambut, personally, I don't like this statistic, mainly because of the lack ofinterpretation... for example, it cannot take negative values, hence you can't differentiatebetween positive and negative correlations. It is useful mainly when the twovariables have not been measured at the same locations.Pierre Pierre GoovaertsChief Scientist at BioMedware Inc.Courtesy Associate Professor, University of FloridaPresident of PGeostat LLCOffice address: 516 North State StreetAnn Arbor, MI 48104Voice: (734) 913-1098 (ext. 8)Fax: (734) 913-2201 http://home.comcast.net/~goovaerts/ _ From: owner-ai-geostats@jrc.it on behalf of Peijun LiSent: Wed 9/20/2006 12:35 PMTo: ai-geostats@jrc.itSubject: AI-GEOSTATS: pseudo cross variogram: h=0Dear List,I recently use the pseudo cross variogram (PCV) for remote sensingapplications. However, I don't know what does the PCV reflect when lag h=0?As we know, when lag h=0, the (univariate) variogram reflects the nuggeteffect. Is there any similar meaning for PCV? Could you give me somereferences related to PCV?Thanks in advance for reply.Peijun LiPeking University
Re: AI-GEOSTATS: Unbaisedness
No, average of (Z*-Z) is zero average of (sum wZi - Z i)s zero sum wi times average of Z - average if Z =0 if sum w = 1 then this is true, otherwise notSays nothing at all about the average of Z.OK? IsobelDigby Millikan [EMAIL PROTECTED] wrote:BLUE : Best Linear Unbiased EstimatorBest : Minimium error variance. Linear : Linear combination of sample values. Unbiased : E(Z*-Z) = 0 Estimator: An estimateIs unbiasedness a fas? E(Z*-Z) = 0 E(sumwZ(x) Z) = 0 sumwu u =0 says all Z(x) =u this is not true?
Re: AI-GEOSTATS: Re: standardized anomaly
at the data for some phenominum on which one can subdivide. For instance in fluvial (river) deposits different material types, drastically different particle size etc according to what you are studying. I found generally that the lag distance at which the drift commenced was the width of the thinnest horizon in the case of two different populations, but it does not tell you whether it is the top or bottom layer. This must then be done by scrutinization of your data in the vetical plane. Once your data is split you can then do variography on each one of the two layers in the horizontal plane modelling the anistropy of the variance separately, This should only be done once you have again checked these two layers with vertical variograms for drift. If there are more than two populations present then the process can be repeated until all your layers have vertical variograms with no drift and therefore you have split your data correctly. Hope this helps Regards Bill Northrop -Original Message- From: [EMAIL PROTECTED] [ mailto:[EMAIL PROTECTED] <mailto:[EMAIL PROTECTED]>Behalf Of sebastiano trevisani Sent: Monday, August 28, 2006 9:57 AM To: Isobel Clark Cc: ai-geostats@jrc.it Subject: Re: AI-GEOSTATS: Re: standardized anomaly Hi Isobel I would like to use this transformation to deal with a 3D data set characterized by a peculiarity (well, this is quite common!) in the horizontal spatial variability. In particular if I divide the dataset in horizontal layers I see that horizontal variograms show a similar shape but with a re-scaled variance. So, my idea, in order to speed up the process of interpolation, consists to calculate the standardized anomaly for each layer and use the same calculated variogram (well, now it is a kind of standardized variogram calculated using all layers)) during interpolation with a 3D routine. Yes, in reality this is only a trick ...because I`m simply performing a series of 2D interpolations along layers. This because of, once the data have been transformed, it is not reasonable to use during interpolation samples coming from different horizontal layers. Sincerely Sebastiano At 14.06 25/08/2006, Isobel Clark wrote: Sebastiano You will be fine so long as you actually have a "stationary" phenomenon. That is, there is a constant mean and standard deviation over your study area -- no trends, no discontinuities, no changes of behaviour. Such a transformation also assumes that your data follow a fairly symmetrical histogram. Your semi-variogram will look exaclty the same as your 'raw' data semi-variogram but should have a sill around 1. Isobel http://www.kriging.com Sebastiano Trevisani <[EMAIL PROTECTED]>wrote: Dear list member A procedural question for you... I'm thinking to transform my data in a standardized anomaly [i.e. (raw datum- sample average)/sample standard deviation)] and then I`ll perfom the geostatistical analysis on these transformed data. At first glance, I don't see problem in the back-transformation of interpolated data and in the correct evaluation of estimation variance. Am I wrong? Sincerely Sebastiano + + To post a message to the list, send it to ai-geostats@jrc.it + To unsubscribe, send email to majordomo@ jrc.it with no subject and "unsubscribe ai-geostats" in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/ ++ To post a message to the list, send it to ai-geostats@jrc.it+ To unsubscribe, send email to majordomo@ jrc.it with no subject and "unsubscribe ai-geostats" in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list+ As a general service to list users, please remember to post a summary of any useful responses to your questions.+ Support to the forum can be found at http://www.ai-geostats.org/
AI-GEOSTATS: Re: standardized anomaly
SebastianoYour standardisation produces a mean of zero and a standard deviation of 1, without changing the characteristics of the semi-variogram (range, relative nugget effect etc.)I presume you will standardise each 'layer' separately? Then use a 3D search which does not include samples from layers above and below the current one. Sounds very neat and efficient if your layers are flat and horizontal. Yes, I would definitely try that and see what you get. Let us know!All the best Isobel http://www.kriging.com
AI-GEOSTATS: Re: standardized anomaly
SebastianoYou will be fine so long as you actually have a "stationary" phenomenon. That is, there is a constant mean and standard deviation over your study area -- no trends, no discontinuities, no changes of behaviour. Such a transformation also assumes that your data follow a fairly symmetrical histogram. Your semi-variogram will look exaclty the same as your 'raw' data semi-variogram but should have a sill around 1.Isobel http://www.kriging.comSebastiano Trevisani [EMAIL PROTECTED] wrote: Dear list memberA procedural question for you...I'm thinking to transform my data in a standardized anomaly [i.e. (raw datum- sample average)/sample standard deviation)] and then I`ll perfom the geostatistical analysis on these transformed data. At first glance, I don't see problem in the back-transformation of interpolated data and in the correct evaluation of estimation variance. Am I wrong?SincerelySebastiano++ To post a message to the list, send it to ai-geostats@jrc.it+ To unsubscribe, send email to majordomo@ jrc.it with no subject and "unsubscribe ai-geostats" in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list+ As a general service to list users, please remember to post a summary of any useful responses to your questions.+ Support to the forum can be found at http://www.ai-geostats.org/
AI-GEOSTATS: Re: Detrending the heads
RajniYou could download our free tutorial from the site http://www.kriging.comThere are lots of ways to detrend the data, this illustrates one of the simpler ways.IsobelRajni Gaur [EMAIL PROTECTED] wrote: Dear List members,I am working on the kriging of piezometric head data using the othersecondary variable as an external drift.I need to remove the trend from the piezometric head data but i dontknow how to detrend the data set. Please guide me for this procedure?thankyou in advanceRajni++ To post a message to the list, send it to ai-geostats@jrc.it+ To unsubscribe, send email to majordomo@ jrc.it with no subject and "unsubscribe ai-geostats" in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list+ As a general service to list users, please remember to post a summary of any useful responses to your questions.+ Support to the forum can be found at http://www.ai-geostats.org/
Re: AI-GEOSTATS: Log versus nscore transform
YettaIf you have sub-populations, the lognormal backtransform probably wouldn't work very well -- this is one place where cross validation is extremely valuable. There are many methods of 'decomposing' mixed distributions. P.D.M. Macdonald has a nice shareware program using a maximum likelihood method. I like probability paper, but then I'm an old age pensionerIsobel http://www.kriging.comYetta Jager [EMAIL PROTECTED] wrote: Regardless of how well a lognormal model represents the distribution of the (one realization) of data,there are still significant issues in interpreting back-transformed kriging predictions and their back-transformedvariances. For example, because the back-transformed mean is a function of both the transformed mean and kriging variance, higher estimates result where kriging variances are higher (ie areas with lower density of sampling data). Does this make sense? Or just choose to model the median instead of the mean.I was advised to consider identifying different sub-populations with possible different means and variances as separate strata, which can be standardized by their individual variances and the residuals kriged (or simulated) together. We have one example (on my website) of where we developed a method to do this. Also, consider using covariates to reduce the variation in residuals first. YettaAt 11:37 AM 8/10/2006, you wrote: Mike, I can't speak to EPA UCLs, and I'm too far removed from the literature at this point to make a cogent argument... but I do remember my work characterizing the hydraulic properties of artificial soils and there was no doubt that the soil water retention curves (tension vs water content) were log normal. I also remember Wilford Gardner (UW-Madison) commenting on how often that function form appeared in soil water physics. While digging through an old folder I found a classic reference ...Spatial Variability of Field-Measured Soil-Water PropertiesDR Nielsen, JW Biggar and KT ErhHillgardia Vol 42, Number 7, pp 215-260, Nov 1973MaribethAt 08:50 AM 8/10/2006 -0400, Michael Grant wrote: My apologies. The email below accidentally only went to Gregoire only. It turns out that I haven't quite reconnected to the list correctly.. So...--- Original Message - From: Michael Grant To: Gregoire Dubois Sent: Wednesday, August 09, 2006 8:48 AMSubject: Re: AI-GEOSTATS: Log versus nscore transformHi Gregoire,Please forgive the rambling philosophical response but I find your question interestingly provocative.Is a preference of lognormality mathematical elegance or is it tradition? I remember an era of virtually automatic assumption of lognormality for two key classes of variables in our business (nuclear/environmental): contaminant concentrations and hydraulic conductivity. That practice lingers. By the early and mid 1990's many human and ecological risk assessors assumed lognormality of contaminant concentrations in environmental media as an article of faith. 'The data are skewed and hence lognormal.' In the US, I suspect that this state of affairs reflected in part the issuance of a single document--the USEPA's approachable supplemental guidance on calculating UCL for human health risk assessment (May 1992). While the EPA clearly evolved beyond that point, e.g., the agency's work on bootstrapping UCLs, numerical/computational savvy of many but not all 'street' assessors probably lagged. This lag was due in part to a mix of professional focus (toxicology versus numbers), availability of tools, and convenience. Also the commercial environmental business has significantly matured as a class of business and we all know that it is crowded. Competitive pressures are significant, and thorough data analysis--an expensive endeavor--is often a loser. The convenience and economy of sanctioned lognormality (no-one reads the fine print) beckons. For me going beyond nominal practice(?) almost always as been on my time. However, that is the nature of things and as long as we learn...:O) I think that the wider development, elucidation, and/or implementation of computationally intensive techniques, e.g., bootstrap, Monte Carlo, is changing at a fundamental level how we formulate our approaches to many problems, vis-a-vis simulation. (Consider the transparency in the formulation of resampling methods relative to the 'obscurity' of traditional parametric statistics.) Now regarding hydraulic conductivity. Again lognormality is a long-standing tradition of nominal practice. Certainly the last 25 years have witnessed a real evolution of concepts and understanding with respect to hydraulic conductivity. And that evolution certainly continues. But again, a mature, over-crowded environmental business dictates nominal practice. Not everyone is a numbers-oriented (hydro)geologist, and many who compile/interprets conductivity data have other duties/interest. The convenience of long-standing tradition--all theory aside--is powerful when faced
AI-GEOSTATS: Re: generalize kriging variance to average-based estimators different than
OriolDownload for free, my old book Practical Geostatistics. Chapter 4 tells you all about calculating the variance for any weighted average estimator. Follow links from http://www.kriging.comIsobelOriol Falivene [EMAIL PROTECTED] wrote: Dear Colleagues,Im a PhD student working on interpolation of categorical variables(like facies).I would like to know if its possible to generalize the kriging varianceto other average-based estimators different than kriging, such askriging with an areal trend, indicator kriging or inverse distanceweighting?; if its possible could you send me some references where Ican find that?.Thank you.Best regardsOriol--__Oriol Falivene[EMAIL PROTECTED]http://www.ub.es/ggactel. (+34) 93 4034028fax (+34) 93 4021340Fac. de Geologia,Univ. de Barcelona++ To post a message to the list, send it to ai-geostats@jrc.it+ To unsubscribe, send email to majordomo@ jrc.it with no subject and "unsubscribe ai-geostats" in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list+ As a general service to list users, please remember to post a summary of any useful responses to your questions.+ Support to the forum can be found at http://www.ai-geostats.org/
AI-GEOSTATS: Re: special case of ordinary cokriging
Hi MaartenShort answer is simply, No. If both variables are sampled at exactly the same location, introducing the secondary variable isprobably introducing more variation into your kriging rather than more information.IsobelMaarten De Boever [EMAIL PROTECTED] wrote: Dear all,The potential improvement of cokriging depends on the extend to which the secondary variable has been sampled additionally to the primary.Is there any difference between ordinary kriging and ordinary cokriging in the situation where all observations of the primary and secondary variable are located at the same locations? Will ordinary cokriging have in that situation any advantage over ordinary kriging?Thanks in advantage,De Boever Maarten.-- ir. Maarten De BoeverResearch Group Soil Spatial Inventory Techniques (ORBIT)Department Soil Management and Soil CareFaculty of Bioscience EngineeringGhent University Coupure 653, 9000 Gent, BelgiumTel. + 32 (0)9 264 6042Fax + 32 (0)9 264 6247e-mail : [EMAIL PROTECTED]http://www.soilman.ugent.be/orbit ++ To post a message to the list, send it to ai-geostats@jrc.it+ To unsubscribe, send email to majordomo@ jrc.it with no subject and "unsubscribe ai-geostats" in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list+ As a general service to list users, please remember to post a summary of any useful responses to your questions.+ Support to the forum can be found at http://www.ai-geostats.org/
AI-GEOSTATS: Effects of spatial autocorrelation on descriptive statistics
ChaoshengIf you are only describing your samples, such concepts as random and independent are irrelevant. They apply to the use of your sample statistics to estimate population parameters. If all you want to do is describe your samples, you can calculate any statistics you like.However, you talk about "normality" and "outliers". These concepts depend on teh notion of a population from which the samples were drawn. If you are trying to estimate the parameters of that population, then dependence and non-randomness are as important as potential outliers and the shape of the population.The "optimal weighted average" is usually known as "ordinary kriging" provided there is no significant trend. ;-)Isobel http://www.kriging.comChaosheng Zhang [EMAIL PROTECTED] wrote: Dear Isobel,Thanks for the helpful reply. In fact, I have been waiting for a reply fromyou. -:)I think the questions are fairly well answered by you. However, I want tomove a step forward or perhaps backward.A question "forward": What are the methods to calculate the "optimalweighted average"? Are they widely accepted/used/cited?A question "backward": Do we really need to care about if the data arespatially correlated or not, when we calculate descriptive statistics eventhough we are aware of such an issue? Results calcuated from only thenon-correlated samples (e.g., sill in a variogram) really reflect the "true"values of statistics? Generally we only care about outliers andnon-normality. In the spatial context, we care about sampling clusters.Otherwise, we still have to use conventional statistics.Best
regards,Chaosheng- Original Message - From: Isobel ClarkTo: Chaosheng ZhangCc: ai-geostats@jrc.itSent: Thursday, May 25, 2006 3:59 PMSubject: AI-GEOSTATS: Re: Effects of spatial autocorrelation on descriptivestatisticsChaoshengSome thoughts in response to your questions:1: "Spatially correlated data provide redundant information for thecalculation of mean"I would not say "redundant". Even if information is correlated, thecorrelation is not perfect (=1) which would be "redundant". If the data isspatially correlated, the correlations should be included in the choice ofweight for each sample and in the calculation of the 'standard error' andconfidence levels. An optimal weighted average of spatially correlated datawill always give a better answer than a smaller subset on non-correlateddata.As an example, you might try kriging a large block with a set of
(internal)samples spaced at the range of influence and then repeat the exercise with ahandful of samples between these 'independent' ones.2: "In the presence of spatially correlated data, would a dispersionvariance . be the proper calculation for the measure of variance?"The obvious answer is "yes and no". If by dispersion variance you mean thestandard calculation of variance:Sum(g_i - gbar)^2/(n-1) often calculated as{Sum(g_i^2)/n - gbar^2}/(n-1)where g_i represents each sample value and gbar the arithmetic mean of allsamples, then No, it is not appropriate.The proper calculation for dispersion variance of a spatially correlateddata set includes all the cross-covariances, not just the squares of samplevalues. It also requires a better estimate of the population than gbar (see1 above). If you are looking for descriptive statistics, then the dispersionvariance can be calculated using the
'middle term' from the full estimationvariance -- the gamma-bar(S_i,S_j) term.In prectice, the most appropriate (and probably simplest) estimate of the'population' dispersion variance in the presence of spatially correlateddata is the total sill on the semi-variogram model. This is, theoretically,the dispersion variance as calculated from samples which are non-correlated.IsobelChaosheng Zhang <[EMAIL PROTECTED]>wrote:AI-GEOSTATSMove of the list to [EMAIL PROTECTED]Dear All,I'm looking for answers to effects of spatial autocorrelation onconventional descriptive statistics. More specifically, any comments on thefollowing statements?1. "Spatially correlated data provide redundant information for thecalculation of mean";2. "In the presence of spatially correlated data, would a dispersionvariance . be the proper calculation for the measure of variance?"Best
regards,Chaosheng Zhang--Dr. Chaosheng ZhangLecturer in GISDepartment of GeographyNational University of Ireland, GalwayIRELANDTel: +353-91-492375Fax: +353-91-495505E-mail: [EMAIL PROTECTED]Web1: www.nuigalway.ie/geography/zhang.htmlWeb2: www.nuigalway.ie/geography/gis+ To post a message to the list, send it to ai-geostats@jrc.it+ To unsubscribe, send email to majordomo@ jrc.it with no subject and"unsubscribe ai-geostats" in the message body. DO NOT SENDSubscribe/Unsubscribe requests to the list+ As a general service to list users, please remember to post a summary ofany useful responses to your questions.+ Support to the forum can be found at http://www.ai-geostats.org/
AI-GEOSTATS: Re: Effects of spatial autocorrelation on descriptive statistics
ChaoshengSome thoughts in response toyour questions:1: "Spatially correlated data provide redundant information for thecalculation of mean" I would not say "redundant". Even if information is correlated, the correlation is not perfect (=1) which wouldbe "redundant". If the data is spatially correlated, the correlations should be included in the choice of weight for each sample and in the calculation of the 'standard error' and confidence levels. An optimal weighted average of spatially correlated data will always give a better answer than a smaller subset on non-correlated data.As an example, you might try kriging a large block with a set of (internal) samples spaced at the range of influence and then repeat the exercise with a handful of samples between these 'independent' ones.2: "In the
presence of spatially correlated data, would a dispersionvariance . be the proper calculation for the measure of variance?" The obvious answer is "yes and no". If by dispersion variance you mean the standard calculation of variance:Sum(g_i - gbar)^2/(n-1) often calculated as{Sum(g_i^2)/n - gbar^2}/(n-1)where g_i represents each sample value and gbar the arithmetic meanof all samples, then No, it is not appropriate.The proper calculation for dispersion variance of a spatially correlated data set includes all the cross-covariances, not just the squares of sample values. It also requires a better estimate of the population than gbar (see 1 above). If you are looking for descriptive statistics, then the dispersion variance can be calculated using the 'middle term' from the full estimation variance -- the
gamma-bar(S_i,S_j) term.In prectice, the most appropriate (and probably simplest) estimate of the 'population' dispersion variance in the presence of spatially correlated data is the total sill on the semi-variogram model. This is, theoretically, the dispersion variance as calculated from samples which are non-correlated. IsobelChaosheng Zhang [EMAIL PROTECTED] wrote:AI-GEOSTATSMove of the list to [EMAIL PROTECTED]Dear All,I'm looking for answers to effects of spatial autocorrelation onconventional descriptive statistics. More specifically, any comments on thefollowing statements?1. "Spatially correlated data provide redundant information for thecalculation
of mean";2. "In the presence of spatially correlated data, would a dispersionvariance . be the proper calculation for the measure of variance?"Best regards,Chaosheng Zhang--Dr. Chaosheng ZhangLecturer in GISDepartment of GeographyNational University of Ireland, GalwayIRELANDTel: +353-91-492375Fax: +353-91-495505E-mail: [EMAIL PROTECTED]Web1: www.nuigalway.ie/geography/zhang.htmlWeb2: www.nuigalway.ie/geography/gis+ To post a message to the list, send it to ai-geostats@jrc.it+ To unsubscribe, send email to majordomo@ jrc.it with no subject and "unsubscribe ai-geostats" in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list+ As a general service to list users, please remember to post a summary of any useful responses to your questions.+ Support to the forum can be found at http://www.ai-geostats.org/
AI-GEOSTATS: Re: Skewed Distributions
DigbyIf your distribution has a positive skewness as calculated (bulks towards zero with long tail into high value) the proportion below the mean will be significantly higher than 50%. If negatively skewed -- e.g. Calcium in limestone, iron in iron ore -- more than 50% will be above the mean.The arithmetic mean is the equivalent of the centre of gravity -- one sample way out on the arm outweighs loads of samples close to the centre.Welcome all to the new list IsobelDigby Millikan [EMAIL PROTECTED] wrote: Is it correct that the probability of being above or below the mean of a skewed distribution is not necessarily 0.5?
[ai-geostats] Re: Regional estimation - block kriging or conditional simulation?
Tom Would it be wise to state that if you only want the mean and variance = use block kriging, if you want a pdf = use conditional simulation? Oh, yes, please do. There are two ways to apply "discretisation". One is to estimate each of the fine grid of points and store the weights for each sample. You can then aggregate (average) the estimates and compute the estimation variance for the overall average. This has been suggested by Cressie and can also serve for non-Normal distributions and their back-transforms. Takes a lot of computer time, but not nearly as much as simulation. Has the advantage of only using the short part of the semi-variogram model and the disadvantage of having to compute the estimation variance.The other way is to directly krige the block average - one kriging system, one estimate with its associated kriging variance. Has the advantage of being very fast, with the disadvantages of potentially large sparse matrices and using all of your semi-variogram model. The sparse matrix problems have been well discussed by such experts as Don Myers in Math Geol. It is a common fallacy to trust the short distance semi-variogram and assume that model fit decreases with distance. In most cases, the bulk of pairs included in a semi-variogram graph are in the middle to larger distances - unless you go past the generally accepted distance of one-half maximum of study area. Models are actually most reliable in the middle. If you doubt this, try watching the (in)sensitivity of the Cressie goodness of fit measure when you change the nugget effect - and, hence, the initial slope of your model. Isobel http://courses.kriging.com* By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] RE: kriging without a nugget
Hello allThe real issue here is not what your philosophy is but what your software does with the semi-variogram model at zero distance.There are (to my knowledge) two possibilities in current software packages: (a) force the model to go through zero at zero distance, that is gamma(0)=0(b) allow the model to hit the vertical axis, that is gamma(0)=nugget effectOption (a) makes kriging an exact interpolator. If you krige exactly at a sample location, you will get the sample value and a kriging variance of zero. This is what Matheron orignally specified and will be found in all of the early geostatistics text books.Option (b) means that kriging will not exactly 'honour' your data, but will put the most weight on the sample and some weights on the other samples. If you have software that runs on option (b) the only way to honour your sample values is to have a zero nugget effect.You do not have to remove the nugget effect from your model, just add another (say spherical) component to your model whose sill equals the real nugget effect and whose range of influence is below your closest sample spacing. If you do not know which option is implemented in your software, run a kriging with nugget effect is and with this alternative. If there is no difference in the results, your software does option (a) gamma(0)=0. As discussed in the other emails, nugget effect includes all 'random' variation at scales shorter than your inter-sample distances -- measurement errors, reproducibility issues and short scale variations. Measurement and reproducibility/replication errors can be quantified by standard statistical analysis of variance methods such as described in any experimental design textbooks. Remember, in this case, that it is the 'errors' that need to be independent of one another -- not the actual sampled values. Small scale variation can only be addressed by closer sampling, for example the famous geostatistical crosses.If you can quantify "sampling errors" and have (b)-type software, you can use a combination where a short-range spherical (say) replaces the smaller scale variability and the nugget effect reflects the 'true' replication error. It is then your choice as to whether you filter out the replication error by removing that nugget effect from your model.An important point to bear in mind is that if you use (b)-type software and/or remove the nugget effect when kriging, your calculated kriging variances will be too low by a factor of 2*nugget effect. If you divide the nugget effect as suggested, your kriging variance will be too low by a factor of 2*replication error. One more comment: some packages analyse and model the semi-variogram but use a covariance (sill minus semi-variogram) when kriging. It is odds-on that these packages will be type (b). Isobel http://www.kriging.com/courses* By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Software for Automatic Semivariogram Estimation
Thanks Behrang, I see you are using Cressie weights. Isobel http://uk.geocities.com/drisobelclarkBehrang Kushavand [EMAIL PROTECTED] wrote:Dear Prof. Clark Here is thepaper: http://www.ansinet.org/fulltext/jas/jas581405-1407.pdf Formula (4) is the weight factor. King regards. Behrang.- Original Message - From: Isobel Clark To: Behrang Kushavand Cc: AI Geostats mailing list Sent: Tuesday, February 28, 2006 9:53 PM Subject: [ai-geostats] Re: Software for Automatic Semivariogram EstimationBehrangWhat weighting do you use in the weighted least squares?Isobel http://www.kriging.comBehrang Kushavand [EMAIL PROTECTED] wrote: hi,I have a software for Variogram AUTO Modeling (winvam) that works with gslib(GAMV.exe).First you must calculate experimental variogram (omni or directional) withgamv.exe and then by using winvam, you can fit the best model by leastsquare and weights least square criteria for given model(s),You can find it at:http://www.ai-geostats.org/software/Geostats_software/WinVAM.htmKing regards.Behrang.- Original Message -From: "Edzer J. Pebesma" <[EMAIL PROTECTED]>To: "Mach Nife" <[EMAIL PROTECTED]>Cc: "ai-geostats" <AI-GEOSTATS@UNIL.CH>Sent: Tuesday, February 28, 2006 7:59 PMSubject: Re: [ai-geostats] Software for Automatic Semivariogram Estimation Mach Nife wrote: Hi, I'm hunting for a software (freeware/openSource if possible), that would help estimating the best possible semivariogram curve in a non-interactive way. As an example, ArcGis Geostatistical Analyst does a pretty good job at this when we accept the defaults. It does some automatic calculations for the parameters of the selected model. I've tried Gstat "Fit" method (in the command-line version), but the results aren't what I expected. What I need is a command line software or one that can be controlled by programming. Any ideas? Some. I did have a look at your data, and at the ArcGIS fit window you sent me. Clearly, we do not fully agree on what is to be considered a "good" job. ArcGIS calculates semivariances up to the largest distances present in your data set; afaik the general recommendation is not to look further than half the longest distance (compare acf computation in time series); the gstat default is one third the diagonal of the area spanned. Have you tried modifying any of these defaults? Interval widths? When looking at the fit, it seems that ArcGIS shows a couple (4?) directional variograms in a single plot, but apart from that, the sample variogram suggests a linear model. It is obvious that fitting three parameters (exponential model with nugget) to something that tends to be linear will lead to problems -- an infinite set of solutions, for instance. When you insist on having an exponential model, you could for instance force the range to a certain (large) value. I suspect ArcGIS stops adjusting the range of the exponential model when it exceeds the data extent (Constantin, are you with us?), but should that be considered good practice? My experience with automatic, general-purpose automatic variogram fitting are not very positive; if it were, gstat would probably have such a function. Are there other ai-geostats readers who have positive or negative experiences with, or who routinely trust, automatically fitted variograms? Which software? Looking forward to a heated debate, -- Edzer machnife __ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or inthe body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or inthe body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm )* To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED]Signoff ai-geostats* By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm )* To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED]Signoff ai-geostats * By using the ai-geostats mailing
[ai-geostats] Re: Software for Automatic Semivariogram Estimation
Hi AllIt is difficult to have an automaticbest fit semi-variogram until you define what you mean by "best fit". Noel Cressie's goodness of fit statistic goes a long way towards the ideal, but is very insensitive to changes in nugget effect and pretty insensitive to fairly large changes in the ranges. Optimal Cressie fits aren't always optimal visually, either.None of the automated methods I've heard of will choose the type of semi-variogram model and/or the number of nested components. Or anisotropy for the most part.As Ed says, if we knew the criteria we'd all write software for it (and retire!). I also look forward to varied opinions. Semi-variogram fitting is one of the most subjective stages of a geostatistical analysis.Isobelhttp://www.kriging.com* By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: Software for Automatic Semivariogram Estimation
EdI use the Cressie statistic to four significant figures as a guide in the interactive fitting, but generally end up using a visual judgement. It tracks as you drag the model around, so you can watch it change.I think the 'real' visual objective function is probably the perpendicular (to tangent) distance to the model line, which is effectively thecombination of both gamma and h. One should then be able to alter the relative weighting between distance and height. Haven't tried this yet.Isobel http://www.kriging.com* By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: Some simple questions
Jan, you sent this to me personally not to the list - although you may have posted it earlier to the list and I din't see it.You lost the right to my response when you turned down my invitation 12 years ago. Your relentless attempts to denigrate a subject simply because you do not understand it does not improve the situation.I repeat my invitation. Come down to Reno, sit in my course, learn the answers to your questionsand put your point of view when appropriate. You might also want to study the differences in the use of English between North America and the dry humour of Scotland. Isobel http://www.kriging.com/coursesJW [EMAIL PROTECTED] wrote: Hi Everybody,As a compassionate person who is married to a granny I would not want to scramble anybody's brain so I keep my questions simple enough to understand them myself. What I would want most of all isanswers to the following questions:Why is the real variance of a SINGLE distance-weighted average replaced with the pseudo kriging variance of a SET of kriged estimates? Visit ai-geostats.org, go to Documents/JW_Merks, look at the Excel template titled "Bre-X and the Kriging Game", and compare the statistics of two widely-spaced lines of salted boreholes with those for three lines of kriged boreholes. Could kriging possiblycreate spatial dependence where it doesn't exists? Next, look at the Excel template titled "Clark and the Kriging Game", and figure out what happens when Clark's coordinates are replaced with coordinates beyond the sample space defined by her set of hypothetical uranium concentrations . Examine whether or not Clark's ordered set displays a significant degree of spatial dependence by applying Fisher's F-test. Note how degrees of freedom change from positive irrationals to positive integers when the distance-weighted average converges on the arithmetic mean and its variance on the Central Limit Theorem as all weighing factors converge on 1/n.That is not too difficult to understand but what about testing for spatial dependence. One or othergeostats doctrine dictates that spatial dependence may be assumed , unless proved otherwise. How about that? I wouldn't mentionitifI couldn't post the proof on my website! AndMatheron didn't even teach his disciples how to prove otherwise!!! Why is spatial dependence assumed rather than verified by applying Fisher's F-test? Visit ai-geostats.org, go to Documents/JW_Merks, look at the Excel template titled "Bre-X Bonanza Borehole", and find out how Fisher's F-test proves not only that the ordered set of Bre-X's bogus gold grades displays a significant degree of spatial dependence but also that the intrinsic variance of Busang's gold is statistically identical to zero just the same.I could have proved that the intrinsic variance of Busang's phantom gold is statistically identical to zero on the basis of three to five boreholes and twenty to thirty duplicate gold assays for crushed and salted 2.9 m core sections. I shall prove that in due course. Some of you are unconvinced that the kriging game is about to grind to a halt, and that drum beating about the Wits bush is futile. After all, it is a scientific fraud to assume, krige, smooth and rig the rules of mathematical statistics.J W Merks * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
Re: [ai-geostats] spherical model
Hi, I do not know whether you received any answers off-list, so here goes.The "spherical" model of geostatistics was so-named by Matheron and is sometimes also known as the Matheron model. His idea was that a sample has a 'sphere of influence' around it. Potential (or actual) samples within this sphere have values which are 'related' to the value at the central point. Imagine, now, a second such point with its own sphere of influence. If the spheres do not touch, there is no relationship between the values at the two central points. If the spheres overlap, there will be a relationship. The more the spheres overlap, the stronger the relationship. The spherical semi-variogram is the simple geometric calculation for the volume of NON-overlap of the two spheres, given the distance between their centres. There is no real reason why it should work in so many cases -- any more than there is for the Normal (Gaussian) distribution being found so often in nature. In fact, there is often a possibility to fit several of the semi-variogram models in practice. You could decide which is most appropriate using something like Cressie's goodness of fit test (analagous to a sort of chi-squared statistic).Isobel http://uk.geocities.com/drisobelclark"M. Nur Heriawan" [EMAIL PROTECTED] wrote: Dear list,I have small query. Why almost all kind of spatialdata set (ore grade data, sea surface temperaturedata, soil thickness, etc.) is fitted to the spherical(variogram) model? May anyone explain the origin ofthis spherical model?Thank you for your help.Regards,M. Nur Heriawan---Graduate School of Science and TechnologyKumamoto University Kurokami 2-39-1, Kumamoto 860-8555, JAPAN * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: Geostats Scam continued
O boy, I wish my world included the kind of data which would allow modelling of anisotropy on a 10m scale! I am full of envy.Isobel http://www.stokos.demon.co.ukEdward Isaaks [EMAIL PROTECTED] wrote: Hello ListFYI, a few comments related to the ongoing discussion re Geostats Scam.Stephen Henley makes some valid points on the shortcomings of geostatistics.In particular, I have also been troubled by the application of models"invariant under spatial translation" to real world data."The proper selection of data" for estimation is considered by many to bethe fundamental mantra of ore resource estimation. Typically, the selectionof data for variography and the estimation of block model grades iscontrolled through manually interpreted models of lithology, alteration,grade shells, structural domains and so on. Although these models arepractical at the scale of the deposit, they are not practical at localscales where local scale is defined by distances as short as 10 m, overwhich abrupt changes in the direction of geologic trends such as grade,fault direction, fracture patterns, and rock type contacts are observed.Obviously, it is not practical to control the selection of data at thisscale using manually interpreted models. However, the good news is that the proper selection of data for kriging canbe achieved at a local scale by aligning an anisotropic search ellipsoidwith the local geologic trend(s) on a block by block basis. The idea is simple. Before each block is estimated, the anisotropy ratios ofthe local search neighborhood are adjusted and the axes aligned with localtrends in the data. The method has come to be known as local anisotropykriging or LAK. The results are remarkable. I have an example where LAKapplied to grade control out performs ordinary kriging by reducing dilutionand ore loss. You can read more about this relatively new implementation ofan old idea by visiting www.isaaks.com and clicking on "Geo Docs".I would also add a note regarding popular geostatistical misconceptions, andthere are several. For example, Krige, Deutsch, Vann and many others havepublished papers admonishing conditional bias. However, in miningapplications (where geostatistics has its roots) conditional bias isactually irrelevant, unless the estimates are used for grade control. See"The Kriging Oxymoron" at www.isaaks.com "Geo Docs" for a peer reviewedpaper on the subject. I recently read a paper by J Vann, S Jackson, and O Bertoli (2003) thatactually proposes a method for designing the kriging search neighborhoodbased on minimizing conditional bias. Horrifying - do they not realize thatsuch practice actually increases the estimation error of the predictedtonnes and grade above cutoff? This paper is probably the worst (best?)example I have seen of a faulty misconception in 25 years of ore resourceassessment. One can almost understand why geostatistics might be labeled ascam. However, I'm not sure I agree with Stephen where he appears to suggest thatthe "vast array of methods and an array of intensely mathematical publishedpapers" are somewhat responsible for providing the means to deliver"whatever the client wants". The difference between a professional and anamateur practitioner is knowing which is the correct tool for the job andhow to use it properly. I'd argue that a packed toolbox is not the problembut rather, the inexperienced or dishonest practitioner is the problem.And finally, I have done some research on the subject of computing "weightedvariances" since a number of "weighted variance" estimators can be found inthe literature including Mr. Merks' version. Each of the estimators I foundprovided a different estimate of the weighted variance and to make mattersworse, not one was shown to be a valid statistical estimator -- they weresimply stated without derivation(see footnote). However, the good news isthat with careful work and with help from Colin Daly and Don Myers, I nowhave the mathematical derivation of an unbiased estimator for the populationvariance given a sample of N (iid) observations with associated weights.Now, it turns out that in spite of all the huffing and puffing by ourcolleague Mr. Merks, the "weighted variance" estimator that he so loudlychampions is biased under the iid model! Perhaps Mr. Merks' time could havebeen better spent looking for an unbiased variance estimator rather thanstalking the "lost variance". :-)A copy of this work will be made available to the list followingpublication. Derivation -- A logical or mathematical process indicating through asequence of statements that a result such as a theorem or a formulanecessarily follows from the initial assumptions. Edward IsaaksReferenceJ Vann, S Jackson and O Bertoli, (2003), "Quantitative Kriging NeighbourhoodAnalysis for the MiningGeologist - A Description of the Method With Worked Case Examples", 5thInternational Mining Geology
[ai-geostats] Re: More on geo-stats
Jim (cc Fran!)Thanks for the long email. I think grandmother-hood must be scrambling my brains because I am not following some of your logic. Or maybe it is the after-effects of trying to thump sense into the heads of those shareholders ;-)It is most probable that Jan Merks got involved in this field in the first place because someone tried to horn in on his sampling theory expertise. He has written some awesome stuff on the problems of the sampling/assay process. I have had the privilege of being peripherally involved with that end of the business through Norman Lotter, currently at Sudbury and finishing his PhD on just this probability plot/sampling bias/mineralogical interpretation stuff. See joint paper at 2000 SME (http://uk.geocities.com/drisobelclark/resume follow publications link).However, I am a mining engineer. It is my job to take the sample results, no matter how much they suck and give the engineers some indication of where and when they might mine in order to obtain payable ore. I have been doing this job since way before I learned any geostatistics. In fact, my first ever job was to produce 'correction factors' to allow a hydrothermal tin mine to predict their mining grades from their development grades. I only discovered later that the common sense methods I applied were identical to those produced by Sichel and Krige in the early 1950s in South African gold mines (also nothing to do with geostatistics). This job was extremely straight forward as the only issue was how to predict the average grade of 3,000 tonnes of rock from around 50 kilos of sample. The interesting parts of that work were the things I discovered in the numbers which the geologists forgot to tell me about. Like: three phases of mineralisation; a bloody great fault through the middle of the vein; grades falling off at depth and rising at shallows. Read my 1974 IMM paper to see where I got my basic training -- and all pre-geostats. YESyou should be doing geology and mineralogy first -- or hydrology, climate analysis, entymology or whatever your equivalent is. YES, statistical or geostatistical or any numerical analysis should enhance and support this analysis. In my experience, the second most common phrase I encounter is "oh! we didn't think that was important!". In my courses I use examples of where geostatisticans have mucked(?) up a resource evaluation because they ignored the geology. I also use examples where the geologists did the same because their interpretation of the geology was inappropriate. I also use examples where I knew intuitively something was wrong but couldn't for the life of me explain why until I managed to browbeat the client into given me the information they "didn't think was important". You don't find this stuff in the textbooks.Geostatistical methods are not a scam. They are just another way of looking at your sample data and trying to draw inferences from the data.They may be inappropriate for your application. They may be used by unscrupulous individuals. They may be used by resource evaluators who aregullible enough to trust the data given to them by the client. The scam of BreX wasn't perpetrated by the geologists, the assay labs or the geostatistics. The scam of BreX was perpetrated by the bastard who put handfuls of alluvial gold in the samples on site and robbed the shareholders blind. It isn't the resource evaluators who are now living in the Cayman Islands on the proceeds of shares which went to $250 and crashed overnight. Geostatistical methods have their strengths and weaknesses, as do all interpolation methods based on real data. I don't see anyone writing emails about the "Bicubic splines scam?" or the "triangulation mapping method scam?" or the "join up the top and bottom of the ore zone with a fuzzy pencil scam?" or the "save the wavelets scam?". If you are uncertain of which approach you should apply, use your common sense. Ask these questions of any technique:- what are the basic assumptions? - are the algorithms and/or software technically adequate? - do the results make sense?Apart from anything else, the above process will make it easier for you to explain to other people (like your defence committee) why you chose (or didn't choose) those methods. Think for yourself and don't dismiss a technique because someone has made it his/her life's work to attack it -- especially if they present no alternative way to do the job. Isobel http://www.kriging.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: Geostats Scam?
Hi Mach (?)Jan Merks is a consultant with a formidable and well-earned reputation in sampling theory and applications. I understand he sits on many committees in Canada which define standards for sampling and evaluation. The first of his "geostatistics scam" articles appeared under the title "Geostatistics or voodoo statistics" in 1992, in just about every mineral industry publication from the Engineering Mining Journal to the Northern Miner newspaper. In this article hereferences Michel David's book (1978) and my 1979 book Practical Geostatistics. In December 1993, after considerable pressure from my colleagues and many more publications of this article, I wrote a personal letter to Dr Merks inviting him to come down to Reno, Nevada and put his thoughts at a short course I was about to teach. I have now put both of these faxes up on the Web at http://www.kriging.com/correspondence so that you can judge for yourselves what the position was then. Please forgive the quality of the reproduction as thermal fax paper tends to fade with time!Since then, Dr Merk's has made it his life's work to visit every site possible (e.g. Amazon) and post negative reviews and comments about geostatistics. His comments are coherent and persuasive and have influenced many people, like yourself, against this whole field.His premise is that statistical theory does not apply to auto-correlated or spatially related variables.This will come as an unpleasant surprise to all statisticans involved in the study of stochastic variables including such authors as Sir David Cox (Emeritus Professor of Statistics, Imperial College London and author of the basic textbook in stochastic processes), Noel Cressie (Director of Spatial Statistics at Ohio State University)and even Brian Ripley (Professor of Statistics at Oxford University) -- not to mention Roger Mead (now retired, formerly Head of Department of Applied Statistics at Reading University, England) who taught me spatial statistics in 1969 before I'd ever heard of geostatistics. Make no mistake, there areflaws ingeostatistics both as a theory and in application. There is plenty of room for improvement across the spectrum and(hopefully) people around the world are working on this as we read. There are also advances in other approaches to spatial estimation which I (for one) watch with interest in the anticipation of new tools for the real world.Criticism should be seen as a good thing and an aid to development. However, relentless negativity serves no-one on either side of this non-discussion. An exchange of ideas is more profitable than an endless stream of insults on either side. In the meantime? Learn what you can and judge for yourself whether the ideas of geostatistics make sense in practice and could be applicable to your own problems. Isobel Clark http://www.kriging.com/courses * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: Normal score transform for conditional sequential simulations
PaulHave you considered doing your analyses in two stages:(a) presence/absence indicator where all values other than zero become '1' and you are effectively analysing the probability of presence (or absence) at your estimated or simulated points?(b) normal score transform or whatever on your actual "value if present"The combination of the results from (a) and (b)might give you a better handle than trying to include the zeroes as part of the same distribution. We have had some pretty good results using this approach on birds and bugs, so it might well work with fish!Isobel http://www.kriging.com/coursesPaul Walline [EMAIL PROTECTED] wrote: Ive been a lurker for a while, and have learned a lot from reading thediscussions, so thanks in advance for that.My question concerns the use of the normal score transform when makingrepeated conditional sequential Gaussian simulations using GSLIB. I believethe criticism that the backtransform would give biased results (as discussedin the Saito and Goovaerts 2000 paper in the discussion about Multi-GausinanKriging) does not apply to simulations because at each point to besimulated, a single normal score value is drawn at random from the cdfobtained by kriging. The averaging takes place in the original data space. Icame to this conclusion from trying to figure out how I could apply thecorrection described in the Saito and Goovaerts paper.But even if the above is true, I may still have a problem because of thehigh percentage of zeros in my data sets, which ranges from 4 to 22%. I(the GSLIB program actually) rank these zero values randomly and I dontknow how to implement the suggestion (of Goovaerts, citing Verly 1986) ofranking them based on the average value in a search radius so that zerosnear high densities have higher ranks than those in low density areas. Formy purposes, I calculate the total abundance for each realization, and usethe frequency distribution of these totals to calculate empirical confidenceintervals, so Im mostly interested in the variability in these totalabundance realizations. How would the zeros affect this? Someone hassuggested that doing the ranking randomly would increase the nugget effectof the normal score variograms. However, I have 6 data sets and the oneswith the highest % of zeros are not the ones with the largest nuggets. Ifthe nugget has been artificially inflated because zeros are not correlatedafter nscore transform when in fact they are correlated in the raw dataspace, is it reasonable to say that the variability of the simulated totalabundances would be overestimated (and thus conservative)?Cheers,Paul WallineNOAA Fisheries, Alaska Fisheries Science Center* By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm )* To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED]Signoff ai-geostats * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
Re: [ai-geostats] Discrete Gaussian change of support
PerryI don't know about the fancy title, but theoretical change of support for Gaussian (Normal) distributions can be found in Chapter 3 of Practical Geostatistics, which is freely downloadable in lots of formats from http://www.kriging.com/pg1979_download.htmlIsobel* By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: Data on pH from Broom's Barn Farm
ErcanI have a full copy of the BromsBarn data which includes K and P values as well as pH.We got it direct from Dick Webster, but I can supply as text file in CSV or Geo-EAS format.Isobel http://www.kriging.com/whereisshe.htmlercan yesilirmak [EMAIL PROTECTED] wrote:Dear list membersIf available to everyone, would you let me know where I can get the "pH dataof Broom's Barn farm", as used in GSLIB (Deutsch and Journel) and in Geostatistics forEnvironmental Scientists byWebster and Oliver?Regards Ercan Yahoo! for Good - Make a difference this year. * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm )* To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED]Signoff ai-geostats * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: A question on conditional simulations
How many simulations did you do? IsobelAbhijith Titus D'souza [EMAIL PROTECTED] wrote: Hello List:First of all I would like to thank all of you for yourfeedback on my earlier question.Just as an exercise I conducted conditional simulationon my dataset. I used the turning bands algorithmmethod and the sequential gaussian method. While theturning bands method produced a similar map ascompared to IDW and kriging, sequential gaussianproduced an interesting map. It matched the estimationmaps from IDW and kriging only in those neighborhoodswhich contained the sample values. For neighborhoodscontaining no sample values it tended to overestimate,i.e as one went away from the sample values the SGmethod overestimated while the estimation maps didnot.The maps were the average of 100 realizations.Iwas wondering if someone could tell me why thishappens. I am still trying to figure out the theorybehind the simulation methods, but it seems too farfetched for me. ThanksAbhijith __ Yahoo! FareChase: Search multiple travel sites in one click.http://farechase.yahoo.com* By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm )* To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED]Signoff ai-geostats* By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: why do negative kriging values occur
lognormal kriging also solves the problem, where it is appropriate. That is, if your logarithms are close to Normal and cross validation shows that the backtransform is working.
with lognormal kriging, you can happily have negative weights and negative values on the logarithms. The backtransform will always produce positve numbers.
Isobel
http://www.kriging.comArmando [EMAIL PROTECTED] wrote:
Negative weights is a consequence of continuity, thus part of physical and mathematical solution.As point by Gregoire .. when de geometry of points is enough good some points are "masked" .The negative value in the estimator happens when high values receive negative weigths ... and the others are low... !Negative weights are familiar for filter´s users (seismic, geophysics and image)Remember that variogram is a expectation for all the domain thus doesn´t have the responsability to solve local problems. If you have some "rapport" with your data you know that this kind of problem appears in the contact of low values sometimes surround by high values.The king of the negative weights is gaussian model!The solution cited by Gregoire is old for mining users and work very well.Thanks for your
attentionArmandoGregoire Dubois wrote:Negative kriging weights can occur when you have a so-called "screeningeffect", that is points close to the location at which an estimation isneeded "mask" points that are further appart. The problem is thus thetopology of your sampling locations.Solution: reduce the neighborhood of your estimator (e.g. use 1 or 2points in each sector of your serch ellipse to avoid searching too far)A reference explaining the maths behind the weights is: Clayton V.Deutsch, (1996) Correcting for negative weights in ordinary kriging,Computers Geosciences, Volume 22, Issue 7,Pages 765-773.An excellent (free!) tool for visualising this problem is E{Z}-Kriging(see FAQ section of AI-GEOSTATS) written by Denis Walvoort.Hope this
helps,Gregoire__Gregoire Dubois (Ph.D.)European CommissionTel. +39 (0)332 78 6360Fax. +39 (0)332 78 5466WWW: http://rem.jrc.cec.eu.intWWW: http://www.ai-geostats.org-Original Message-From: Abhijith Titus D'souza [mailto:[EMAIL PROTECTED] Sent: 11 November 2005 21:59To: ai-geostats@unil.chSubject: [ai-geostats] why do negative kriging values occurHello List:I'm new to this list and just beginning to get into geostatistics. Itried searching for possible answers on the mailing list, but had noluck. So here I am with my question:My dataset consists of 149 samples(too less ???, butthat is all I have !!) from an offshore area and I amtrying to estimate the grade of a mineral. I used
thesoftware ISATIS for my work. 40% of my data is between0 to 5% with the maximum being 99 %. The data displaysa uniform distribution if we ignore the 40% lowvalues.I tried using gaussian transformation, but tono avail and so stuck with the original data. Thevariogram model did fit well (at least globally)and asI proceeded towards ordinary kriging I got quite a few percentages ofnegative values (3% of the estimated values were negative), with thelowest being -6%. I contacted the ISATIS technical support team and theytold me to play around with the neighbourhood distance and number ofsamples in the neighbourhood etc. After many trial and error runs Ifinally got a nice kriging map but it sill had some negative values(less than 1% of the estimated values) with the lowest being -0.02.I'mcurious as to what could be the reasons behind the negative values. I doget some
negative weights, but is that only reason. Could someone giveme a mathematical and/or intuitive meaning to the negative estimates?Thank you Titus __ Yahoo! FareChase: Search multiple travel sites in one click.http://farechase.yahoo.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm )* To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED]Signoff ai-geostats-- http://www.kadampa.org/portuguese/inspiring_quotes.shtml* By using the ai-geostats mailing list you agree to follow its rules ( see
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[ai-geostats] Re: urgent please
1963 Georges Matheron. Principles of geostatistics. Economic Geology, Vol. 58: p1246--1266 From Statistics for Spatial Data, Noel A.C. Cressie and a google search on "Georges Matheron Economic Geology" ;-) Isobel http://www.kriging.comRajni Gaur [EMAIL PROTECTED] wrote: Dear List members, Can I get the earliest reference of Prof. Matheron in which he proposed the methodology of regionalized variables and claimed that they posses definite structure depending on the spatial correlation, at different locations.IN ENGLISH and not in FRENCHPlease Thanks to all who did the needful to me Regards Rajni* By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm )* To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED]Signoff ai-geostats* By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: Unusual Ordinary Kriging Results
David You seem to have two problems: (1) the Vulcan answer does not match your hand calculation for the same weights and values. (2) you have negative weights. I would think that (1) was of far more concern than two simply because it suggests that the software is not performing the correct calculations. If this block is wrong how about all the rest of them? Maybe you could try a few reasonable looking blocks and see if you can reproduce those answers. If not, Vulcan and all users need to know that the software has a bug! It is possible you have something like 'affine transformation' or recoverability factor switched on. Does Vulcan do stuff like that? This would produce results outside the range of the data and not equal to weight times grade calculation. On (2), opinions differ about negative weights. With your well behaved data and very small negative weights you are unlikely to get values substantially outside the range of the samples. Witness your own calculation. If negative weights worry you, reduce your search radius until the negative weights become negligible. Does this help? Isobel http://www.kriging.com"Reid, David W" [EMAIL PROTECTED] wrote: Hello, After running ordinary kriging estimations using Vulcan mine planning software it wasnoticed there were some unusual estimated grades. I was hoping that someone can confirm that I on the right path + not heading up the yellow brick road to Oz. The estimated value reported/calculated by Vulcan for one block was 80.77. I thought this unusual as thegrade of the 16 samples selected for the estimation range from 51.2 to 65.9 (mean 59.6).I calculated the estimated grade by summing the products of sample grade and sample weight(given by the software) and got a value of 60.13 which seems far more reasonable. Maptek the software vendor's response was to suggest that negative weights were responsible for thehigh estimation. Details of the samples are below. Have Ioverlooked something in my calculation oris theresome otherexplanation for the result? Regards David Reid Number X Y Z Grade Distance weight weight * grade 1 51325.6 19954.3 205.28 64 8.755 0.316811 20.27589 2 51325.6 19954.3 206.8 64 12.751 0.047555 3.043512 3 51310 19953.7 206.95 65.9 15.699 0.097072 6.397071 4 51308.2 19968.6 206.58 51.2 19.183 0.078537 4.021086 5 51309.4 19970.1 206.67 63.9 19.557 0.05828 3.724066 6 51325.3 19939 205.08 58.2 19.948 0.08432 4.907436 7 51310 19939.3 204.78 55.1 21.197 0.117351 6.466049 8 51325.3 19977.5 204.98 56.7 21.267 0.182511 10.34838 9 51310.3 19938.7 204.88 60 21.646 0.085906 5.154343 10 51325.3 19939 206.6 58.2 21.843 -0.03607 -2.09928 11 51310 19939.3 206.3 55.405 22.767 -0.00408 -0.22581 12 51325.3 19977.5 206.5 56.7 22.98 0.028131 1.59505 13 51310.3 19938.7 206.4 60 23.259 -0.02124 -1.27434 14 51309.4 19970.1 208.9 62.3 24.395 -0.0517 -3.22108 15 51340.2 19939 205.48 61 28.172 0.040817 2.489816 16 51340.2 19939 207 61 29.772 -0.0242 -1.4764 TOTAL 1 60.12579 Ave 59.60031 block estimate 80.77 David Reid This message and any attached files may contain information that is confidential and/or subject of legal privilege intended only for use by the intended recipient. If you are not the intended recipient or the person responsible for delivering the message to the intended recipient, be advised that you have received this message in error and that any dissemination, copying or use of this message or attachment is strictly forbidden, as is the disclosure of the information therein. If you have received this message in error please notify the sender immediately and delete the message.* By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm )* To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED]Signoff ai-geostats* By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
Re: [ai-geostats] back transformation
What back-transform would you use for (1)? I use Sichel's theory, which produces prediction intervals for the lognormal back transform. Download any one of my lognormal kriging papers from http://uk.geocities.com/drisobelclark/resume (late 1990s, various audiences). IsobelRecep kantarci [EMAIL PROTECTED] wrote: Dear list members Whenstudied on alog-transformed variable and intended toconstruct prediction intervals, whichoption should be followed? Why? 1) construct prediction interval first, back-transform later. OR 2) back-transform first, construct prediction interval later. Thanks in advance Recep Yahoo! kullaniyor musunuz?Simdi, 1GB e-posta saklama alani sunuyorhttp://tr.mail.yahoo.com* By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm )* To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED]Signoff ai-geostats* By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: Why degree of freedom is n-1
Hi Eric
What complications! You should find, in any basic statistical inference that the correlation is divided by (n-1) and has (n-2) degrees of freedom.
The logic behind this is because the correlation is actually calculated as the covariance divided by the two standard deviations.
The covariance is calculated from n PAIRS of samples, not 2n individual observations andhas (n-1) degrees of freedom because it uses the pair of means(m1,m2) as its centroid.
Dividing by the pair (s1,s2) loses you the other degree of freedom. Tests on the correlation have (n-2) degrees of freedom.
If you use (say) a regression relationship with 'k' coefficients including the constraint of the means, you lose k degrees of freedom. Any book which deals with 'Analysis of variance' will explain this for you. We use exactly this approach fortesting a trend surface (see free tutorial at http://geoecosse.bizland.com/softwares or download my SNARK (1977) paper from http://uk.geocities.com/drisobelclark/resume).
Hope this helps.
Isobel[EMAIL PROTECTED] wrote:
This follow-up is slighlty aside the subject line of the mailing list, butas a geologist, this is the only statistically-flavoured one I amsubscribed to. Therefore :Federico Pardo <[EMAIL PROTECTED]>said: Having N samples, and then n degrees of freedom. One degree of freedom is used (or taken) by the mean calculation. Then when you calculate the variance or the standard deviation, you only have left n-1 degrees of freedom.Apart a rigorous calculation I am aware of that in this very case (cf.Peter Bossew's contribution on the same thread, that details it), gives aproof for this rule-of-thumb, what more or less rigourous statisticaldevelopments gives consistance to it ?I mean, for the empirical correlation coefficient,rhoXiYi = SUM_i=1..N( (x_i - mx).(y_i - my) / sx / sy ) / WHAT_NUMBERMust
WHAT_NUMBER be, for a kind of unbiased estimate ("a kind of" meaning"with some eventual Fisher z-transform"...):* N for simplicity,* N-2 as I have most frequently seen in books that dare give this formula(N points, minus 1 for position and 1 for dispersion ?),* or 2N-4 -- 2N for the (x_i,y_i), minus 4 for {mx,my,sx,sy} -- as astrict application of the rule-of-thumb seems to suggest ?And what about, when fitting for instance a 3-parameter non-linearfunction, reducing the number of degrees of freedom, to N-3 (number ofpoints, minus one for each function parameter ? I have never read any kindof explanation to support it, though it seems widely Thanks in advance for enlightments or simply tracks for other resources ofexplanations.-- Éric L.* By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm )* To unsubscribe to ai-geostats, send the
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[ai-geostats] Re: Need Your Advises on Books
Hi Reza The best 'geostatistics' book I know in oil is Mike Hohn's Geostatisticsand Petroleum Geology. There is also Geostatistics for Natural Resources Evaluation by Pierre Goovaerts, which got pretty good reviews. Isobel Reza Nazarian [EMAIL PROTECTED] wrote: Dear ExpertsI am going to order some Geostatistical Books. I need them for self training and need to contain numerical examples and practices. I have already ordered Practical Geostatistics written by Isobel Clark. It would be highly appreciated.if you could please advise me more specially on books with trend in Oil Reservoir.Waiting for your suggestions.Very Best RegardsReza NazarianGeophysicist* By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm )* To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED]Signoff ai-geostats* By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
RE: [ai-geostats] modelling trend and kriging type
Perry Your basic semi-variogram graph has a parabola added to it. Shoots off upwards (usually) at some distance. If the distance is large (past the range of influence) you can ignore it. See some of our mid-80s papers on the Wolfcamp data whichlots ofpeople use as a teaching set now. Or read my free tutorial at http://geoecosse.bizland.com/softwares(kriging with trend). Isobel[EMAIL PROTECTED] wrote: Hi all I may know this already, but what are the symptoms of data with a trend? What is the difference between a dataset with a trend and a non-stationary dataset? Cheers Perry Collier Senior Mine Geologist Ernest Henry Mine Xstrata Copper Australia Ph (07) 4769 4527 Fx (07) 4769 4555 E-mail [EMAIL PROTECTED] Web http://www.xstrata.com PO Box 527 Cloncurry QLD 4824 Australia "Light travels faster than sound. That is why some people appear bright until you hear them speak" -Original Message- From: Pierre Goovaerts [mailto:[EMAIL PROTECTED]] Sent: Friday, 1 July 2005 12:54 AM To: Recep kantarci; ai-geostats@unil.ch Subject: RE: [ai-geostats] modelling trend and kriging type To add to the excellent comments by Edzer and Gregoire, 1. Universal kriging = kriging with a trend. The second terminology has been proposed by Andre Journel who felt that the term "universal" was vague and misleadingly "ambitious". 2. Kriging with an external drift (KED) is mathematically the same as universal kriging (UK). Secondary variables are simply replacing the spatial coordinates used in UK. 3. Regression kriging denotes all the techniques where the trend is modeled outside the kriging algorithm. There are various methods that can be used to model that trend, ranging from linear regression to neural networks. Kriging is used to interpolate the residuals. In practice these techniques have more flexibility than universal kriging in term of modeling the trend: multiple variables either categorical or continuous can be incorporated easily and many sofwtare are available for this trend modeling. The only limitation is that the trend is modeled globally (i.e. the regression coefficients are constant in space) while in KED the coefficients are reestimated within each search window. Cheers, Pierre Pierre Goovaerts Chief Scientist at Biomedware 516 North State Street Ann Arbor, MI 48104 Voice: (734) 913-1098 Fax: (734) 913-2201 http://home.comcast.net/~goovaerts/ -Original Message- From: Recep kantarci [mailto:[EMAIL PROTECTED]] Sent: Thu 6/30/2005 9:38 AM To: ai-geostats@unil.ch Cc: Subject: [ai-geostats] modelling trend and kriging typeDear ai-geostats members When the data used has a trend, it is needed to model trend and in this case there exists various types of kriging to apply (universal kriging, kriging with a trend, regression kriging etc). If this is the case, does one should use the same type of kriging or different depending on modeling the trend using coordinates of target variable or using other (namely, secondary or auxillary) variables such as elevation or topography ? That is , are there a dinstinction depending on the type of variables to model the trend while kriging? Best regards Recep _ Yahoo! kullaniyor musunuz? Istenmeyen postadan biktiniz mi? Istenmeyen postadan en iyi korunma Yahoo! Postaâda http://tr.mail.yahoo.com http://tr.mail.yahoo.com/ ** The information contained in this e-mail is confidential and is intended only for the use of the addressee(s). If you receive this e-mail in error, any use, distribution or copying of this e-mail is not permitted. You are requested to forward unwanted e-mail and address any problems to the Xstrata Queensland Support Centre. Support Centre e-mail: [EMAIL PROTECTED] Support Centre phone: Australia 1800 500 646 International +61 2 9034 3710 ** * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm )* To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED]Signoff ai-geostats* By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] RE: Treatment of gold outliers from belt samples
I am a little worried by the statements:" As you point out, the sub-sample values should have a normal distribution. Increasing the number of samples (n) would help. " Averages of lognormal (or other highly skewed) data are not Normal. The lognormal, in particular, does not conform to the Central Limit Theorem. This is why Sichel in the South African GoldMines and Finney in the Royal Statistical Society worked out the lognormal estimation theories. There are two issues here, I think: (1) the sampling issue which uses a small aliquot to represent a large bulk of sample (2) the estimation of an average value from highly skewed data -- or, if your prefer, data with the odd erratic high. It was (2) that inspired Sichel to do his work. (1) is the province of such experts as Gy and Merks. For those readers unfamiliar with South African Gold values, it is perfectly possible for neighbouring 'chip' samples to be two orders of magnitude different in value whether in situ or on a conveyor belt. It is less common but still perfectly feasible for bulk samples. Similar characteristics occur in hydrothermal veins and other 'erratic' geological environments. This is not a sampling issue but fact. There are sampling and assaying issues, of course, and much has been published on this topic. I had the honour to be junior (very) author on a paper with Norman Lotter on this topic. This paper can also be downloaded from my personal site at http://uk.geocities.com/drisobelclark/resumeNorm provides a lot of references which you might find useful. Isobel * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
Re: [ai-geostats] Treatment of gold outliers from belt samples
Hi Kevin Can I refer you to the works of Herbert Sichel which was developed exactly for this problem, earliest paper Trans Inst Min Metall 1949. Or you can download my 1987 SAIMMpaper from http://uk.geocities.com/drisobelclark/resume which describes Sichel's work. Isobel http://geoecosse.bizland.com"Kevin Lowe (Office Park)" [EMAIL PROTECTED] wrote: Hi, How should one treat obvious gold grade outliers from samples collected from a belt? The sampling is carried out by an automatic belt sampler prior to the ore being milled. The samples are collected and stored in a bin until there is approximately 1 ton of sample. The bin is then sent off to a lab which crushes and splits the 1 ton bin sample to produce 8 separate samples which are then assayed. Assuming there are no issues with the lab procedures, how should one treat a very high value? For example purposes, say the 8 samples returned grades (g/t) of 2.8, 4.6, 5.2, 4.5, 35.6, 3.6, 4.2, 4.7. The arithmetic mean for the eight is 8.15g/t but if the one high grade is removed the arithmetic mean is 4.23g/t. Should I simply exclude the high value or should I cut the value of the sample to some arbitrary value (say the upper 95% confidence limit)? Although individual chip samples collected from the orebody, for the purposes of evaluation, are highly skewed, the samples from the bin approximate a normal distribution (excluding the high value). I look forward to any comments or perhaps direction to papers or web sites on this topic. Many Thanks Kevin Lowe This e-mail message has been scanned for Viruses and Content and cleared by NetIQ MailMarshal * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm )* To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED]Signoff ai-geostats* By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
Re: [ai-geostats] ...how to distinguish different form of stationarity...
Simone Under the intrinsic hypothesis you can have a semi-variogram (bounded or unbounded) if the data is non-stationary. Generally we assume a stationary mean when calculating a semi-variogram to simplify the calculation. If the mean is not stationary, you have to include a drift or 'trend' in your calculation. The data has to be stationary inthe mean to have a covariance function simply because you have to subtract the mean to get a covariance. This is theory. In practice you can always calculate the covariance, you just assume a constant mean. This does not guarantee that it is in any way meaningful. If the mean is not stationary, you will get a parabola added to your 'real' semi-variogram graph. This is the universal sign of significant drift or trend. Your semi-variogram can be unbounded without going parabolic - see, for example, linear and power models. Ifthe variance of the data is non-stationary, you may still have intrinsic stationarity. The usual example used in the text books is a 'random walk' or Brownian motion. The test for intrinsic stationarity is obtaining a meaningful semi-variogram when you calculate it. You can also try jack-knifing - leave out some of your data and see if the semi-variogram still looks similar. Isobel http://www.kriging.com (under construction) * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] RE: A banal question...
Simone
Not so banal a question. 34 years ago my supervisor
gave me some papers to read which said exactly that.
Even with a Master's in applied statistics, I could
not make head-nor-tail of the explanation. So I went
on a three week short course at Fontainebleau and they
explained it around the middle of the third week!
A very simplistic explanation: when you calculate an
ordinary covariance you have two columns of figures,
say variable g and f. The covariance between g and f
is calculated (in practice) by multiplying the two
columns together, summing the results and then
subtracting the product of the two means. Difficult to
do in a text email but:
Sum(g x f)/n - mean(g) x mean(f)
This is exactly equivalent to:
Sum (g-mean(g)x(f-mean(f))/n
{leave out the whole n or (n-1) debate at this point)
In a geostatistical context, g would be the value of a
sample (any sample). f would be the value of another
sample a specified distance away. That is, specify one
particular distance (h), find pairs of samples that
distance apart, first sample in pair is g (first
column), second sample in pair is f (second column).
Calculate covariance as above with the modification
that the mean of g and the mean of f will be the same.
Repeat for many different distances and you end up
with a graph of how the covariance of the values
varies with the distance between the samples.
I, personally, prefer the semi-variogram approach
because it is a lot easier to explain! Also, you do
not need to know (or estimate) the mean. More
explanations in free downloadable Practical
Geostatistics 1979,
http://uk.geocities.com/drisobelclark/practica.htm.
If you have second order stationarity, the covariance
function is simply the sample value variance minus the
semi-variogram.
Does this help?
Isobel
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[ai-geostats] Re: Who is J. W. Merks???
Jan Merks is an expert in sampling theory and works as an independent consultant out of Vancouver, Canada. He has a web site which I don't have to hand, where all of these opinions are repeated and amplified. Jan first starting publishing anti-geostatistics articles in 1991 or 1992 and the article Geostatistics or Voodoo Statistics appeared in every mining publication from the Engineering and Mining Journal to the Northern Miner newspaper. He republishes every so often and had one a few years ago in the Mining Journal on April 1st. The articles start with a quotation from Tolstoy to the effect that even the most intelligent of people can turn a blind eye to facts that don't fit their own world view. It is ironic that he does not realise this quotation is apropriate to his own world view too. His basic premise is that geostatistics is a con job foisted on an unsuspecting industry by consultants trying to rip them off for large sums of money. He supports this view by pointing out that the semi-variogram is divided by the number of pairs of samples (N) and not by N-1 when every statistician knows that variances are divided by N-1 not N. The point missed here is that variances are divided by N-1 because we estimate the population mean. Semi-variograms are not divided by N-1 because we assume the population mean (difference) to be zeto and do not estimate it. His second point is that kriging with (say) k samples should have k-1 degrees of freedom. This is not true becuase the variance/covariance or semi-variogram terms used in the kriging system are based on the total number of pairs used in the construction of the graph. I once asked Noel Cressie about this and he said that the degrees of freedom in the kriging system would be n(n-1) where n is the total number of samples in the data set. Back in 1992, I invited Dr Merks to come down to a course I was giving in Reno to put his point of view and debate it with myself and the students and staff at University of Nevada-Reno. I still have his letter on file. It basically says, I don't see the point you aren't going to listen anyway. Before you ask, the only reason I did this was because his articles referred to only two geostatistical publications: Michel David's Mining Geostatistics and my Practical Geostatistics (1979). He also couldn't spell my name right and I wanted to give him the opportunity to change that. It was several years before an editor pointed out to him that there is no 'e' on the end of Isobel Clark. Isobel http://uk.geocities.com/drisobelclark/practica.htm * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: Who is J. W. Merks???
Hello people Thank you for your swift responses, especially on the weekend. This turned out to be a long reply, so feel free to read the next paragraph and skip on to the last one. I think we should be fair to Jan Merks. He got a bee in his bonnet over an issue which is less than well explained in the bulk of geostatistics text books, especially 13 years ago. He tried discussing it with some geostatisticians and got the usual how dare you criticise us reaction from the mainstream. If you don't believe me, get hold of the Engineering Mining Journal and read Danie Krige's response to Merk's article. I have never met Jan Merks and issued my invitation to discussion in the hope that we could learn something from one another. It was turned down with no opening for any continuation of debate, even by email. As a practising mining engineer who has to earn a living valuing mineral resources, I use what works in reality and follow (as much as I am capable of) new theories and practice as they become proven. As Fran says, every orebody is different and uncertainty is part of our way of life. The best we can do is minimise it and quantify what is left, if we can. There are many weak patches in geostatistical theory. However, we are not going to fix them by roaming through Amazon and writing hostile reviews of every book we can find on the topic. Or by ignoring opportunities for discussion and debate. Merks has a very powerful position in Canada, as he sits on the National and Government committees which determine standards for sampling design and such like. He is also, judging by the bulk of his own work, a very intelligent and persuasive communicator. And he is not alone. Read, for example, Philip and Watson's paper in Mathematical Geology in the mid-1980s. It took me several years to figure out why their antagonism to geostatistics was so strong. Finally, after a conversation with a land surveyor in South Africa, I realised that they did not know that we cannot see the surfaces we are mapping -- unlike map makers. Geostatistics is not a panacea and (in my opinion) is not a suitable method for automated mapping. Not till we patch the weak places, like semi-variogram modelling, conditional bias and handling non-Normal data. However, until someone comes along with something that is as easy to understand, test and apply I am sticking with it. I never wrote a response to Merk's article. How can you take a guy's criticism seriously when he can't bother to spell your name right? Isobel (with an o) Clark (without an e) http://geoecosse.bizland.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] matter of pronunciation
Dutch-fashion, where the g is a kind of throat-clearing sound, More like the ch in the Scottish loch or like the greek letter chi which forms the first letter in Christos. If you want to be pedantic, the technique was not named kriging by Matheron but krigeage - a attempt to turn krige into a noun. This is pronounced with a very soft 'g' almost a 'sh' sound. Most of the other 'foreign' versions use a hard 'g': krigaggio, krigovanie kriggage (quebecois) and so on. Almost everyone I know use the short 'i' as in pig. Isobel http://geoecosse.bizland.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] matter of pronunciation
Colin As a personal style, I tend to use a capital when referring to (say) Ordinary Kriging, Indicator Kriging and so on and a small letter when used as a noun or verb: the area was kriged Isobel http://uk.geocities.com/drisobelclark * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: A matter of pronunciation
Even stranger when you consider that the Rev Bayes refused to have his work published during his lifetime. Isobel http://geoecosse.bizland.com/whatsnew --- Wilmer Rivers [EMAIL PROTECTED] wrote: In reports, should kriging, kriged, and krige be written with an uppercase K, or lowercase as shown here? Poor Mr. Krige. It seems that the people who calculate the Lagrangian multipliers for Bayesian kriging must hold mathematical physicists and even mathematically inclined clergymen in higher regard than they do lowly mining engineers. A capital offense, surely! :) Wil * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Definition of standardize variograms
Gregoire Michel David coined the term relative semi-variogram back in the 70s for what I think you mean by general relative -- that is, each lag is divided by the square of the mean of the samples used at that lag. Gary Raymond proposed the pairwise relative soon after. I used the type you are describing where the whole semi-variogram is divided by the same mean-squared in my 1979 paper (Does Geostatistics Work) because I was analysing a line of samples where all samples are used at every lag. The term standardised in general statistics usually means dividing through by the variance or standard deviation (not a mean). This is the first time I have seen it in context with a semi-variogram. Seen with no other information, I would have taken this to imply standardised to total sill of 1. This would mean dividing by the variance, not the mean-squared. Relative semi-variograms help you avoid the proportional effect if you are trying to calculate a semi-variogram on positively skewed data. Noel Cressie wrote a paper in Mathematical Geology (early 90s?) which showed that the David relative semi-variogram was topologically equivalent to using logarithms. You data does not have to be lognormal to do this. Computationally, taking logarithms is faster and more stable than relative semi-variograms. Probably why most people don't bother. Gary Raymond provides software for the pair-wise and Geostat Systems will have relative semi-variograms. Don't know of any free stuff. Isobel http://geoecosse.bizland.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: Automatic Kriging
What I don't understand is, how to, automatically, calculate all the parameters (Sill, Range, Nugget) and fit the perfect model so it produce a as sharp as possible result. All you need to do is be able to define perfect! Please please let me know if you do - then I can finally retire ;-) You could do worse than start by optimising the Cressie goodness of fit statistic. This incorporates a lot (but not all) of the criteria for a perfect semi-variogram fit. Isobel http://geoecosse.bizland.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: question about kriging with skewed distribution
Ruben (et al) It is true that Matheron's theory is based on no distributional assumptions. In fact, there is no requirement for the distribution to be the same at every location in the study area. The necessity for using traditional geostatistical theory is that the 'difference between two values' should have a common distribution for a specified distance (and possibly direction). The form of this distribution is irrelevant but it needs to possess a mean and variance. The problem lies not with the theory but with the practice. If you have the whole 'realisation' you can calculate the true average and variance and the shape of each distribution is irrelevant. If you have only a few samples, then you can only find estimates for the means and variances at each distance. If the underlying distribution is highly skewed then, unless you have ideal conditions (large number of samples, regular sampling locations), your estimate of the variance will be unstable -- influenced by the average of the samples included in the particular estimate. There was a huge amount of debate about this proportional effect back in the 70s [search for 'relative semi-variogram']. So, you have two potential problems: (1) you may not get any true picture of the semi-variogram due to the uncertainty associated with each point exacerbated by the proportional effect; (2) you may not wish to use an averaging technique such as kriging on skewed samples. All of Sichel's (mining) and much of Krige's work was motivated by the fact that local averaging is not sensible when your data has a coefficient of variation greater than around 1. The theory is terrific, witness its survival for over 40 years and its proliferation over many fields of application. However, real life isn't so tidy at the sharp end ;-) Isobel http://geoecosse.bizland.com/whatsnew.htm * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: question about kriging with skewed distribution
Marek Although theoretically non-point support has no reason to be lognormal, in practice it very often is. We have had good results in estimating areas and volumes, although we have limited experience with non-point support of any significance. You can test the persistency of lognormality by aggregating your (point?) sample values into larger units or by simulation. If you seek something theoretically sound you could use a model based on your 'point' samples to simulate aggregates and investigate the distributions which result. Noel Cressie has done quite a bit with aggregated values. I do not have references to hand but I am sure a search would turn up some interesting stuff. Isobel http://geoecosse.bizland.com/whatsnew.htm * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: example in practical geostatistics
Annelies I hope I do not offend anyone on the list by answering this question. Anyone who does not have the book can download it free of charge from http://uk.geocities.com/drisobelclark/practica.htm Chapter 4 is dedicated to explaining the concept of the estimation variance. In the 'old days' when this book was written, it was felt to be simpler to use examples where all samples were weighted equally to get over the concepts of calculating the extension variance. Only when this was established did we introduce the concept of different weights for each sample. This, then, leads to the development of kriging. You will find this approach in all of the early textbooks and course notes. In Practical Geostatistics, Chapter 5 starts Let us turn, now, to a much more common, and probably more realistic, approach to the estimation I admit that Chapter 5 is very brief, but if you take the terms calculated in all of the examples in Chapter 4, you can arrange them in the kriging system and se what weights the samples should have. You will then see that the 'optimal' weighting will be different for different length samples. Isobel http://geoecosse.bizland.com/seasonsgreetings.htm --- Annelies Govaerts [EMAIL PROTECTED] wrote: I have a question about an excercise I found in Practical geostatistics (Isobel Clark). In chapter 4 they look at the estimation variance of some, theoretical, examples. One of the examples is a 2D panel (30m at 40m). They use the average grade of two drives, (one along the side of 30 m en one along the side of 40m) to estimate the value inside the panel. (for those who has a texbook the excercise is on pages 80-84). I found it a bit strange to use samples with different lengths? And why doesn't they get different weights in the formula for the estimation variance? So even when you have a more extreme case where you have a 1m by 40 m panel you should not taking in account this difference in length of the two drives? Thanks, Annelies * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: Correlogram estimate
Jack I find Edzer notation confusing, since evryone I know uses C0 for the bugget effect not the total sill of the semi-variogram model. The correlogram relationship is a theoretical one but should hold provided the paricular gamma(h) is calculated using all the same samples at the total sill. According to Noel Cressie (Statistics for Spatial Data) the Cauchy Schwartz inequality should hold for every point on the calculated semi-variogram subject to all samples being used at the lag. You are probably getting greater than 1 because of clustered sampling (?) or non-Normality in your data. Isobel --- jack webster [EMAIL PROTECTED] wrote: Hi Thank you, for replying, but as you know the theorical relation between variogram and correlogram r(h) = (C0-gamma(h))/C0 does not holds for estimates! I compute correlogrm with r^(h) = (C0^-gamma^(h))/C0^ (^ = estimate notation) but in some lags r^(h) was grater than 1 !! Sincelely: webster === --- Edzer J. Pebesma [EMAIL PROTECTED] wrote: jack webster wrote: hello, I need a good estimator for the Correlogram, under 2nd stationary condition, and a SPLUS program for computing it (if there is). Sincerely: Webster Jack, you can use the S-Plus function acf() to compute autocorrelations from one-dimensional data. As you're on this list, you probably want it for 2-D or 3-D. For those data you can compute variograms. In S-Plus, library gstat (free; www.gstat.org) or the S-Plus SpatialStats module (commercial) are available for computing sample variograms and modelling variogram functions. The correlogram can be computed from a variogram by r(h) = (C0-gamma(h))/C0 with C0 the sill of the variogram and gamma(h) the semivariance (model) value. -- Edzer * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats __ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
Re: [ai-geostats] Re: Correlogram estimate
Edzer PS -- what was that bugget? :-) Sorry, keyboard a bit congested ;-) nugget effect C0, total sill C(0)! Isobel * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: descriptive statistics or inference?
Digby The variance/sill relationship is theoretical and does not depend on the layout of the samples, regular or clustered. Since the sill only uses pairs where samples are uncorrelated from one another, the clustering is irrelevant. It does depend on the distribution of the samples values being 'stationary', that is having constant mean and variance over the study area. It also depends on that distribution having a valid variance. For example, the variance of samples from a lognormal distribution depends on the average of those samples - hence the proportional effect. All of this is explained in any basic geostatistics book, including Matheron's original Theory of Regionalised Variables and my Practical Geostatistics (Chapter 3) which cn be freely downloaded from http://geoecosse.bizland.com/practica.htm Isobel http://uk.geocities.com/drisobelclark/seasonsgreetings.htm * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] within line variance
Meng-Ying Assuming that you generated your line with a Spherical model, range 3, 27 samples making 9 ranges the variance within that line will (theoretically) be 0.9191 of the semi-variogram sill. Of course this theory depends on you have every possible sample in that length, not just 27 of them. Isobel http://uk.geocities.com/drisobelclark/practica.htm * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] variogram analysis
Rajive I haven't read the other responses yet, so this may be redundant. Two possibilities: (1) anisotropy: if this is shallow marine data there should be a difference between longshore drift and off-shore deepening of sea-bed. You have an omni-directional semi-variogram. It is possible that the sampling grid is irregular enough to be highlighting directional differences?? (2) mega-ripples: I have seen similar behaviour in off-shore marine diamonds which tend to hug the bottom of trenches or ripples. Major ocean beds have mega-ripples on the kilometre scale, which is what you are seeing here. More worrying, I would say, is the fact that your graph is dropping with distance. This suggests that you also have some underlying trend (non-stationarity) which is causing closely spaced samples to be 'more different' than those further apart. I notice you are using a log transform. What does your probability plot look like? Isobel * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: Sill versus least-squares classical variance estimate
Meng-Ying No, I do not think we are communicating. The variance of data values is not affected by correlation between the sample values. The estimated variance for the population IS affected by correlation between the sample values. Statistical inference about the population is based on the assumption that samples were taken randomly and independently from that population. It is the process of estimation of unknown parameters by classical statistical theory which requires these assumptions. Geostatistical inference does not require absence of correlation, quite the contrary. The semi-variogram graph is constructed on the assumption that there is a correlation between samples and that this depends on distance and direction between the pair of samples. If we have a stationary situation, where the mean and variance are constant over the study area, the semi-variogram generally reaches a sill value. The distance at which this happens is interpreted as that distance beyond which the correlation is zero. Sample pairs at this distance or greater can be used to estimate the variance, since the statistical assumptions are now satisifed. Isobel http://geoecosse.bizland.com/whatsnew.htm --- Meng-Ying Li [EMAIL PROTECTED] wrote: Hi Isobel, I understand all points you pointed out, but I'm not sure why the variance should be defined as data NOT SPATIALLY CORRELATED when they may or may not be correlated. Thanks for the clarification, though, I don't think I'd be able to clarify the things you clarifies. You're good. Meng-ying On Wed, 8 Dec 2004, Isobel Clark wrote: Meng-Ying I don't know how to say this any other way. At distances larger than the range of influence, samples are NOT SPATIALLY CORRELATED. The variance of the difference between two uncorrelated samples is twice the variance of one sample around the mean. The semi-variogram is one-half of the variance of the difference. Hence the sill is (theoretically) equal to the variance. The sill is based on all pairs of samples found at a distance greater thn the range of influence. The classical statistical estimator of the variance is only unbiassed if the correct degrees of freedom are used. If the samples are correlated, n-1 is NOT the correct degrees of freedom. All explained in immense detail in Practical Geostatistics 2000, Clark and Harper, http://geoecosse.hypermart.net Did I get it clear this time? Isobel --- Meng-Ying Li [EMAIL PROTECTED] wrote: I understand why it is not appropriate to force the sill so it matches the sample variance. My question is, why estimate the overall variance by the sill value when data are actually correlated? Meng-ying On Tue, 7 Dec 2004, Isobel Clark wrote: Meng-Ying We are talking about estimating the variance of a set of samples where spatial dependence exists. The classical statistical unbiassed estimator of the population variance is s-squared which is the sum of the squared deviations from the mean divided by the relevant degrees of freedom. If the samples are not inter-correlated, the relevant degrees of freedom are (n-1). This gives the formula you find in any introductory statistics book or course. If samples are not independent of one another, the degrees of freedom issue becomes a problem and the classical estimator will be biassed (generally too small on average). In theory, pairs of samples beyond the range of influence on a semi-variogram graph are independent of one another. In theory, the variance of the difference betwen two values which are uncorrelated is twice the variance of one sample around the population mean. This is thought to be why Matheron defined the semi-variogram (one-half the squared difference) so that the final sill would be (theoretically) equal to the population variance. There are computer software packages which will draw a line on your experimental semi-variogram at the height equivalent to the classically calculated sample variance. Some people try to force their semi-variogram models to go through this line. This is dumb as the experimental sill is a better estimate because it does have the degrees of freedom it is supposed to have. I am not sure whether this is clear enough. If you email me off the list, I can recommend publications which might help you out. Isobel http://geoecosse.bizland.com/books.htm --- Meng-Ying Li [EMAIL PROTECTED] wrote: Hi Isobel, Could you explain why it would be a better estimate of the variance when independance is considered? I'd rather think that we consider the dependance when the overall variance are to be estimated
[ai-geostats] descriptive statistics or inference?
And just a personal opinion, I would like to think geostatistic theories apply to population of any size, as small as 27, or as large as 1,000,000. If I'm making an example that geostatistics doesn't apply, then there's something to concern about in this approach. Geostatistics applies to any size of sample set but for the theory to work ou have to have a relatively enormous population to draw rom. Put in plain terms, the assumption is that the withdrawal of the samples does not materially affect the behaviour of the population. If you have the whole population, you don't need to do tests or estimates. Isobel http:geoecosse.bizland.com/books.htm * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
Re: [ai-geostats] Re: F and T-test for samples drawn from the same p
Digby I see where you are coming from on this, but in fact the sill is composed of those pairs of samples which are independent of one another - or, at least, have reached some background correlation. This is why the sill makes a better estimate of the variance than the conventional statistical measures, since it is based on independent sampling. Isobel http://geoecosse.bizland.com/whatsnew.htm --- Digby Millikan [EMAIL PROTECTED] wrote: While your talking about sill's being the global variance which I read everywhere, isn't the global variance actually slightly less than the sill, as the values below the range of the variogram are not included? i.e. the sill would be the global variance when you have pure nugget effect. * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Sill versus least-squares classical variance estimate
Meng-Ying We are talking about estimating the variance of a set of samples where spatial dependence exists. The classical statistical unbiassed estimator of the population variance is s-squared which is the sum of the squared deviations from the mean divided by the relevant degrees of freedom. If the samples are not inter-correlated, the relevant degrees of freedom are (n-1). This gives the formula you find in any introductory statistics book or course. If samples are not independent of one another, the degrees of freedom issue becomes a problem and the classical estimator will be biassed (generally too small on average). In theory, pairs of samples beyond the range of influence on a semi-variogram graph are independent of one another. In theory, the variance of the difference betwen two values which are uncorrelated is twice the variance of one sample around the population mean. This is thought to be why Matheron defined the semi-variogram (one-half the squared difference) so that the final sill would be (theoretically) equal to the population variance. There are computer software packages which will draw a line on your experimental semi-variogram at the height equivalent to the classically calculated sample variance. Some people try to force their semi-variogram models to go through this line. This is dumb as the experimental sill is a better estimate because it does have the degrees of freedom it is supposed to have. I am not sure whether this is clear enough. If you email me off the list, I can recommend publications which might help you out. Isobel http://geoecosse.bizland.com/books.htm --- Meng-Ying Li [EMAIL PROTECTED] wrote: Hi Isobel, Could you explain why it would be a better estimate of the variance when independance is considered? I'd rather think that we consider the dependance when the overall variance are to be estimated-- if there actually is dependance between values. Or are you talking about modeling sill value by the stablizing tail on the experimental variogram, instead of modeling by the calculated overall variance? Or, are we talking about variance of different definitions? I'd be concerned if I missed some point of the original definition for variances, like, the variance should be defined with no dependance beween values or something like that. Frankly, I don't think I took the definition of variance too serious when I was learning stats. Meng-ying Digby I see where you are coming from on this, but in fact the sill is composed of those pairs of samples which are independent of one another - or, at least, have reached some background correlation. This is why the sill makes a better estimate of the variance than the conventional statistical measures, since it is based on independent sampling. Isobel * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] RE: F and T-test for samples drawn from the same p
Hence my recommendation to use cross cross validation Isobel http://geoecosse.bizland.com/books.htm --- Colin Daly [EMAIL PROTECTED] wrote: Hi Sorry to repeat myself - but the samples are not independent. Independance is a fundamental assumption of these types of tests - and you cannot interpret the tests if this assumption is violated. In the situation where spatial correlation exists, the true standard error is nothing like as small as the (s/sqrt(n)) that Chaosheng discusses - because the sqrt(n) depends on independence. Again, as I said before, if the data has any type of trend in it, then it is completely meaningless to try and use these tests - and with no trend but some 'ordinary' correlation, you must find a means of taking the data redundancy into account or risk get hopelessly pessimistic results (in the sense of rejecting the null hypothesis of equal means far too often) Consider a trivial example. A one dimensional random function which takes constant values over intervals of lenght one - so, it takes the value a_0 in the interval [0,1[ then the value a_1 in the interval [1,2[ and so on (let us suppose that each a_n term is drawn at random from a gaussian distribution with the same mean and variance for example). Next suppose you are given samples on the interval [0,2]. You spot that there seems to be a jump between [0,1[ and [1,2[ - so you test for the difference in the means. If you apply an f test you will easily find that the mean differs (and more convincingly the more samples you have drawn!). However by construction of the random function, the mean is not different. We have been lulled into the false conclusion of differing means by assuming that all our data are independent. Regards Colin Daly -Original Message- From: Chaosheng Zhang [mailto:[EMAIL PROTECTED] Sent: Sun 12/5/2004 11:42 AM To: [EMAIL PROTECTED] Cc: Colin Badenhorst; Isobel Clark; Donald E. Myers Subject: Re: [ai-geostats] F and T-test for samples drawn from the same p Dear all, I'm wondering if sample size (number of samples, n) is playing a role here. Since Colin is using Excel to analyse several thousand samples, I have checked the functions of t-tests in Excel. In the Data Analysis Tools help, a function is provided for t-Test: Two-Sample Assuming Unequal Variances analysis. This function is the same as those from many text books (There are other forms of the function). Unfortunately, I cannot find the function for assuming equal variances in Excel, but I assume they are similar, and should be the same as those from some text books. From the function, you can find that when the sample size is large you always get a large t value. When sample size is large enough, even slight differences between the mean values of two data sets (x bar and y bar) can be detected, and this will result in rejection of the null hypothesis. This is in fact quite reasonable. When the sample size is large, you are confident with the mean values (Central Limit Theorem), with a very small stand error (s/(sqrt(n)). Therefore, you are confident to detect the differences between the two data sets. Even though there is only a slight difference, you can still say, yes, they are significantly different. If you still remember some time ago, we had a discussion on large sample size problem for tests for normality. When the sample size is large enough, the result can always be expected (for real data sets), that is, rejection of the null hypothesis. Cheers, Chaosheng -- Dr. Chaosheng Zhang Lecturer in GIS Department of Geography National University of Ireland, Galway IRELAND Tel: +353-91-524411 x 2375 Direct Tel: +353-91-49 2375 Fax: +353-91-525700 E-mail: [EMAIL PROTECTED] Web 1: www.nuigalway.ie/geography/zhang.html Web 2: www.nuigalway.ie/geography/gis/index.htm - Original Message - From: Isobel Clark [EMAIL PROTECTED] To: Donald E. Myers [EMAIL PROTECTED] Cc: Colin Badenhorst [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Saturday, December 04, 2004 11:49 AM Subject: [ai-geostats] F and T-test for samples drawn from the same p Don Thank you for the extended clarification of F and t hypothesis test. For those unfamiliar with the concept, it is worth noting that the F test for multiple means may be more familiar under the title Analysis of variance. My own brief answer was in the context of Colin's question, where it was quite clear that he was talking aboutthe simplest F variance-ratio and t comparison of means test. Isobel
[ai-geostats] F and T-test for samples drawn from the same p
Don Thank you for the extended clarification of F and t hypothesis test. For those unfamiliar with the concept, it is worth noting that the F test for multiple means may be more familiar under the title Analysis of variance. My own brief answer was in the context of Colin's question, where it was quite clear that he was talking aboutthe simplest F variance-ratio and t comparison of means test. Isobel * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
Re: [ai-geostats] problem of spatial continuity of groundwater head
Kai I would suggest you take a look at: Introduction to Geostatistics: Applications in Hydrogeology (Stanford-Cambridge Program) P. K. Kitanidis which is a great base to work from. Isobel http:///geoecosse.bizland.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: regularization
Samuel Practical Geostatistics (1979) Chapter 3. Get it for free at http://uk.geocities.com/drisobelclark/practica.htm Isobel http://geoecosse.bizland.com/books.htm * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: Sample data sets
Mark We have about 13 data sets available on our free download site, ranging from mining data to fisheries, agriculture and environmental stuff. Number of data ranges from 27 to 20,000. Download from http://geoecosse.bizland.com/softwares and find details and references for most of them at http://geoecosse.bizland.com/bookbits/Chapter1_PG2000.pdf Isobel ___ALL-NEW Yahoo! Messenger - all new features - even more fun! http://uk.messenger.yahoo.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
Re: [ai-geostats] A question on lag class and lag distance
xhy your questions are long-standing and as yet unanswered in general. 1. How to select the lag class and lag distance in order to obtain a more reasonable experimental variogram? I always think of it as focussing a camera. Believe there is a pattern in your data and our task is to balance 'width of interval' versus 'number of pairs in interval' to get the clearest picture. One of the things I have found most useful with irregularly spaced data is a 'nearest neighbour' analysis. Take each sample and find the closest one to it. Record the distance. Repeat for all samples. This process takes twice as long as calculating the semi-variogram but gives you an idea of the 'natural' or model spacing between your samples. This can be used to guide your choice of interval. Check out our free tutorial downloads at http://geoecosse.bizland.com/softwares 2. Is it reasonable to use an uneven set of lag (e.g. the lag increments are: 0-2.5m, 2.5-5.0m, 5.0-12.0m, 12.0-19.5m, 19.5-27.0m, 27.0-30.0m, 30.0-40m, 40-50m etc.) if a more stable variogram can be obtained? I am not sure I have ever seen this done, but don't see why not if you plot the point at the centre of gravity of your interval (i.e. average distance of pairs found). Hope this helps Isobel http://geoecosse.bizland.com/books.htm ___ALL-NEW Yahoo! Messenger - all new features - even more fun! http://uk.messenger.yahoo.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] spatial relationships
Dear oh Dear, I am failing to communicate (again). As far as I know, I didn't say you could not use geostatistics when a trend is present! I regularly use Universal Kriging for data with a trend and kriging with an external drift when the trend is governed by an outside factor (see free tutorial at website). The question originally posed what how does one decide that geostatistics is not appriate. The answer Gregoire and myself gave was when you cannot get a semi-variogam graph after trying all possible variations of transforms, interpretation and de-trending. I recently worked with an orange grove in Florida (bugs on oranges) which showed no decent semi-variogram even though rough inverse distance maps looked reasonable. It turned out they had two different kinds of tree in the orchard. Separating the 'rootstocks' yielded a vastly improved semi-variogram and decent geostatistical analysis. My additional point was that failure to obtain a semi-variogram model simply means that there is no 'distance related' structure. It does NOT mean there is NO spatial structure. Isobel http://geoecosse.bizland.com/softwares ___ALL-NEW Yahoo! Messenger - all new features - even more fun! http://uk.messenger.yahoo.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: Frightened of Spatial Autocorrelation
Kevin Sounds like an ideal case for Geographically Weighted Regression. You could use semi-variograms or spatial auto-correlation to determine exactly how proximity defines relationship. My only current beef with GWR is the seemingly pre-defined distance weighting functions. Not had much time to get into this yet, so don't dump on me all you experts out there. I would be interested in any published results on this as one of my business partners is doing similar work on bronze age denmark. Isobel http://uk.geocities.com/drisobelclark ___ALL-NEW Yahoo! Messenger - all new features - even more fun! http://uk.messenger.yahoo.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
