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

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• Jan 3, 2005
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
volker.bahn@...
http://www.wle.umaine.edu/used_text%20files/Volker%20Bahn/home.htm-----
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
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
| 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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