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 04469-5755, USA Tel. (207) 581 2799 Fax: (207) 581 2858 [EMAIL PROTECTED] http://www.wle.umaine.edu/used_text%20files/Volker%20Bahn/home.htm----- Original Message ----- From: "jyarus" <[EMAIL PROTECTED]> To: "'Seumas P. Rogan'" <[EMAIL PROTECTED]>; <[email protected]> Sent: Monday, January 03, 2005 12:34 Subject: RE: [ai-geostats] 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= c-bX, 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 | [EMAIL PROTECTED] | 2900 Wilcrest, Suite 370 | Houston, Texas 77042 | tel: (713) 789-9331 | fax: (713) 789-9318 | mobile: (832) 630-7128 | ------------------------------------ | | -----Original Message----- | From: Seumas P. Rogan [mailto:[EMAIL PROTECTED] | Sent: Friday, December 31, 2004 1:14 PM | To: [email protected] | Subject: [ai-geostats] 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 on-line 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 | | | | -------------------------------------------------------------------------------- |* 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
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