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/
Re: AI-GEOSTATS: Moving median
AI-GEOSTATS Dear kai If you don't care about the shape of the moving windows in data metrics grid option of surfer 8 you can calculate the median. Bye Sebastiano At 08.40 24/05/2006, Zosseder, Kai \(LfU\) wrote: AI-GEOSTATS Hello List, Does anybody have experience with moving median technique. I´m looking for a free software or extension for Surfer 8.0, Arcview, ArcGis or R to convert a moving median methods for point patterns (not a moving median filter for raster). Looking forward to help Thanks in advance Kai + 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/
RE: AI-GEOSTATS: multicategory indicator simulation
AI-GEOSTATS Hi Ashton, Sequential Indicator simulation (SIS) is based on the local estimation (i.e. kriging) of the probabilities of occurrence of each of the 7 categories, in your case. Thus, the local mean refers to the local (a priori) probability of occurrence of each of the seven classes based on the calibration of your map. The vectors of local means correspond to the row of your confusion, or error matrix. At the locations of ground-thruthed data, you have non only this vector of local means but also a vector of indicators of occurrence which should include 6 zeros and a one for the category that is observed on the ground. Indicator residuals are computed by subtracting these two vectors. SIS with varying local means is implemented in Gslib program sisim. Cheers, Pierre Pierre Goovaerts Chief Scientist at BioMedware Inc. Courtesy Associate Professor, University of Florida President of PGeostat LLC Office address: 516 North State Street Ann Arbor, MI 48104 Voice: (734) 913-1098 (ext. 8) Fax: (734) 913-2201 http://home.comcast.net/~goovaerts/ From: [EMAIL PROTECTED] on behalf of Ashton Shortridge Sent: Thu 5/25/2006 10:24 AM To: ai-geostats@jrc.it Subject: AI-GEOSTATS: multicategory indicator simulation AI-GEOSTATS Hello all, I have a land cover dataset with codes 1-7 representing different land cover categories. This data is not too good, but might be better than nothing. Let's call this the map. I have a second dataset - a bunch of point locations at which land cover for the area has been ground-truthed. This is essentially my reference data. I can use these things to construct a confusion, or error matrix, like this: [1,] 0. 0.0222 0. 0.867 0. 0.000 0. [2,] 0.0778 0.1889 0. 0.722 0. 0.000 0.0111 [3,] 0. 0.2417 0.4917 0.250 0.0167 0.000 0. [4,] 0.0333 0.2667 0.0667 0.633 0. 0.000 0. [5,] 0. 0.7500 0. 0.125 0. 0.125 0. [6,] 0. 0. 0.9000 0.000 0.1000 0.000 0. [7,] 0. 0. 0. 0.000 0. 0.000 1. where cell i,j corresponds to the observed probability of observing class j on the ground, where class i was present in the map. For example, a cell with class 3 on the map is actually class 3 about 49% of the time. About 24% of the time it's class 2, and 25% of the time it is class 4. Very rarely (1.7%) it's actually class 5. I would like to employ indicator simulation on this data using simple kriging with locally varying means. I want to generate realizations of reference land cover, using the map landcover data to improve the prediction by serving as the mean estimate. This approach is documented in Goovaerts' book and in a paper by Kyriakidis and Dungan (2001). However, several points are unclear to me. First, simple kriging is employed on residuals from the mean. For multicategorical data of the sort I am investigating here, how would one calculate the mean at a particular location? Second and more practically, I've struggled to discover how to implement this in gstat (R version or standalone), and am wondering if anyone has had success with another software package. Thanks in advance for any assistance you can provide. Ashton -- Ashton Shortridge Assistant Professor [EMAIL PROTECTED] Dept of Geography http://www.msu.edu/~ashton 235 Geography Building ph (517) 432-3561 Michigan State University fx (517) 432-1671 Geography Has moved! Map: http://www.rsgis.msu.edu/images/parking-map.gif + 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/
Re: AI-GEOSTATS: multicategory indicator simulation
AI-GEOSTATS Hello Ashton, I would suggest to do the interpolation of the probability field using a logistic scale, to avoid getting negative estimates for some categories. This essentially implies changing your bare zeroes (in the error matrix below) by a suitable small number (say, the smallest probability/10 or so), and take a multivariate logistic transform... details in my thesis (www.tdx.cesca.es/TDX-0123106-122444/index_an.html, or just ask)... we are working in a paper, but it is still on the air... Regards Raimon En/na Ashton Shortridge ha escrit: AI-GEOSTATS Hello all, I have a land cover dataset with codes 1-7 representing different land cover categories. This data is not too good, but might be better than nothing. Let's call this the map. I have a second dataset - a bunch of point locations at which land cover for the area has been ground-truthed. This is essentially my reference data. I can use these things to construct a confusion, or error matrix, like this: [1,] 0. 0.0222 0. 0.867 0. 0.000 0. [2,] 0.0778 0.1889 0. 0.722 0. 0.000 0.0111 [3,] 0. 0.2417 0.4917 0.250 0.0167 0.000 0. [4,] 0.0333 0.2667 0.0667 0.633 0. 0.000 0. [5,] 0. 0.7500 0. 0.125 0. 0.125 0. [6,] 0. 0. 0.9000 0.000 0.1000 0.000 0. [7,] 0. 0. 0. 0.000 0. 0.000 1. where cell i,j corresponds to the observed probability of observing class j on the ground, where class i was present in the map. For example, a cell with class 3 on the map is actually class 3 about 49% of the time. About 24% of the time it's class 2, and 25% of the time it is class 4. Very rarely (1.7%) it's actually class 5. I would like to employ indicator simulation on this data using simple kriging with locally varying means. I want to generate realizations of reference land cover, using the map landcover data to improve the prediction by serving as the mean estimate. This approach is documented in Goovaerts' book and in a paper by Kyriakidis and Dungan (2001). However, several points are unclear to me. First, simple kriging is employed on residuals from the mean. For multicategorical data of the sort I am investigating here, how would one calculate the mean at a particular location? Second and more practically, I've struggled to discover how to implement this in gstat (R version or standalone), and am wondering if anyone has had success with another software package. Thanks in advance for any assistance you can provide. Ashton + 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/
