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1856Re: [ai-geostats] Regression vs. Kriging vs. Simulation vs. IDW

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  • Volker Bahn
    Jan 3, 2005
    • 0 Attachment
      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?




      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
      Original Message -----
      From: "jyarus" <jyarus@...>
      To: "'Seumas P. Rogan'" <sprogan@...>; <ai-geostats@...>
      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
      | 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
      | 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
      | 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
      | 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
      | the values estimated in the upper left quadrant of the map to be
      | overestimated, and those in the lower right to be underestimated. We
      | 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
      | 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) 789-9331
      | fax: (713) 789-9318
      | mobile: (832) 630-7128
      | ------------------------------------
      | -----Original Message-----
      | From: Seumas P. Rogan [mailto:sprogan@...]
      | Sent: Friday, December 31, 2004 1:14 PM
      | To: ai-geostats@...
      | 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


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