RE: [ai-geostats] modelling trend and kriging type

[Gregoire Dubois]

Hi Perry, 

I am curious to see how others will reply to your second question on the
difference between a dataset with a trend and one that is
non-stationary! My reply may sound provocative: you can always remove a
trend when you recognize that there is one. Moving from non-stationarity
to stationarity, on the other hand, can be infinitely more complex (e.g.
moving to non-Euclidean space) 

:)


For what concerns the detection of trends, have a look at the variogram:
a quadratic/exp. increase usually means that there is a trend. Get rid
of the presumed trend and check the variogram of the residuals which
should clearly show a change of structure (if you had a trend
obviously). Quicker might be to use a moving windows strategy to plot
local averages and check if you see any structure (be careful that the
"structure" is not simply an anisotropy of your variable). You could
have a look into the old archives of AI-GEOSTATS. There have been very
nice replies from Donald Myers (see his publications) in the past on
these issues. see http://groups.yahoo.com/group/ai-geostats/ 

Regards

GD



-Original Message-
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] 
Sent: 07 July 2005 03:49
To: ai-geostats@unil.ch
Subject: RE: [ai-geostats] modelling trend and kriging type


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 type 


Dear 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 

  _  
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RE: [ai-geostats] modelling trend and kriging type

[Isobel Clark]

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 which lots of people 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 type             Dear 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! Posta’da     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 
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[ai-geostats] Again on Irf-k...

[Simone Sammartino]

Dear all
I have to thank you for your several references but I must admit I could not 
understand exactly the argument...
My problem is about understanding deeply the differences between UK and IRF-k 
approaches...
It seems both of them see at the variable as the sum of a varying trend and a 
stationary residual; both of them consider such trend as the linear combination 
of monomials in points positions with some specific  coefficients...suddenly 
all the references speak about the conditions for the coefficients of the IRF-k 
approach...that is their sum must be zero...the number of conditions depends on 
the degree of the polynomial trend...if such degree is zero, the only condition 
that satisfies the sum of coefficients equal to zero is that such coefficients 
are 1 and -1...that is the zero order increment or intrinsic approach (the 
stationarity of the increment)...now...
Neither one condition of this kind for UK?!...
Ho to pass from the trend to the conditions?...
Such trend is considered locally (within such neighbourhood) or globally? And 
in UK?...is it considered globally?
The universality condition in UK is exactly the same of the zero order one in 
Irf-k?...what are the differences?
How to introduce, in such framework, the order k intrinsic function?...what is 
it?...the combination of the original non stationary function with the said 
coefficients?...
Why such coefficients should filter higher order trends? In which way?
While in UK is intuitive to understand the concept of trend and residual (I try 
to fit the trend, I remove it from my original variable and I infer variogram 
on the residual), in Irf-k it is not!...
Which is the trend and which is the residual? Is the generalized covariance 
computed on such residual?
Thank you
Simone
-
Dr. Simone Sammartino
PhD student
- Geostatistical analyst
- G.I.S. mapping
I.A.M.C. - C.N.R.
Geomare-Sud section
Port of Naples - Naples
[EMAIL PROTECTED]
-




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