Hi all,
picking up on Jeff's point about collocated cokriging: what is the
difference between this technique (which I'm not familiar with) and an
autoregressive regression models such as CAR, SAR etc?
Thanks
Volker
_______________________________
Volker Bahn
Dept. of Wildlife Ecology  Rm. 210
University of Maine
5755 Nutting Hall
Orono, Maine
044695755, USA
Tel. (207) 581 2799
Fax: (207) 581 2858
volker.bahn@...
http://www.wle.umaine.edu/used_text%20files/Volker%20Bahn/home.htm
Original Message 
From: "jyarus" <
jyarus@...>
To: "'Seumas P. Rogan'" <
sprogan@...>; <
aigeostats@...>
Sent: Monday, January 03, 2005 12:34
Subject: RE: [aigeostats] Regression vs. Kriging vs. Simulation vs. IDW
 Hi Seumas:

 I thought I would throw my 2 cents in regarding a comparison between
kriging
 and linear regression.

 While some of the responses have hit a few important differences, like
 Kriging is a spatial estimator and regression is not, or kriging will
honor
 the original data and regression will not (unless residuals are added back
 in  not often done). For me, the critical point to be made is between
the
 collocated cokriging application and regression. In collocated cokriging,
 like simple regression, two variables are being used, one independent and
 one dependent (of course, this could be expanded to more than one
 independent variable). The object is to predict a value of the dependent
 variable from a relationship established between both the independent and
 dependent observed values. In the ensuing regression equation, there is a
 slope term. For example, in the equation, Y= cbX, c is the intercept and
b
 is the slope. As pointed out by one of the contributors, regression by
 itself is not a spatial estimator, it is a point estimator. As such, the
 equation contains no information about the surrounding data or about the
 relationship between the observed data and the unsampled location where a
 desired estimate of the dependent variable is required. In kriging (or
 cokriging), the slope term "b" is replaced by a covariance matrix that
 informs the system not only about the behavior of the surrounding data
 points and the unsampled location (similar to distance weighting if
 omnidirectional), but also about the spatial behavior within the
 neighborhood  that is, how neighbors are spatially related to other
 neighbors. Thus, the slope term "b" is replaced with a sophisticated
 covariance matrix containing the spatial information.

 The ramifications of using simple regression instead of true spatial
 estimator are significant if the results are presented in map form. While
 this is often difficult to grasp for some, using simple regression as a
 mapping tool will cause geographic portions of a map to consistently be
 overestimated and others underestimated! For example, you may find that
all
 the values estimated in the upper left quadrant of the map to be
 overestimated, and those in the lower right to be underestimated. We
would
 like to believe that a good spatial estimator will be unbiased, and the
 distribution of the error variances over the area of a map will be
uniform 
 no one part of the map will preferentially over or underestimated. The
 bias brought about by the slope term in simple regression can be easily
 tested and proved.

 I have attached a short paper my partner Richard Chambers and I published
in
 the Canadian Recorder a few years back which addressed this issue. The
 article talks about seismic attributes related to petroleum reservoir
 characterization. However, beginning around page 10 or 11, we give an
 example that demonstrates the above points.

 I hope this is informative and useful.

 King Regards,

 Jeffrey M. Yarus
 
 QGSI
 Jeffrey M. Yarus
 Partner

jyarus@...
 2900 Wilcrest, Suite 370
 Houston, Texas 77042
 tel: (713) 7899331
 fax: (713) 7899318
 mobile: (832) 6307128
 

 Original Message
 From: Seumas P. Rogan [mailto:
sprogan@...]
 Sent: Friday, December 31, 2004 1:14 PM
 To:
aigeostats@...
 Subject: [aigeostats] Regression vs. Kriging vs. Simulation vs. IDW


 Hello everyone,

 I apologize if this question is too elementary for this list;
 I want to understand the key differences between linear regression,
 kriging, conditional simulation and other interpolation techniques such as
 IDW or splines in the analyses of spatial data. I would like to know the
 assumptions, strengths and weaknesses of each method, and when one method
 should be preferred to another. I browsed the archives and looked at some
 of the online papers, but they are written at a level beyond my own
 current understanding. It seems to me that this would be a great topic for
 the first chapter of an introductory spatial analysis textbook. Can anyone
 recommend any basic textbooks or references on this topic?
 Any assistance you can offer would be appreciated.

 Sincerely,

 Seumas Rogan





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