- Jan 3, 2005Hi 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

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-----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 - << Previous post in topic Next post in topic >>