Don't assume that the monograph by R. shurtz resolves or

answers the question, it does not.

Part of the problem with the so-called paradox is using

data locations that are all in a 1- dimensional space to

estimate values at locations not in that one-dimensional

space. No interpolation method is going to produce good

results unless additional model characteristics are

assumed to provide for a relationship between the one

dimensional space and higher dimensional space. This

is particularly true if an isotropic variogram/covariance

model is used. With this mis-match in dimensions the

problem is ill-posed.

One way to see the ambiguity is to consider locations on

circles in a plane perpendicular to the the drill

hole axis. Using a an isotropic variogram will result

in the same estimated values at all points on such a

circle. This implies a rather weird physical phenomenon,

i.e., unrealistic.

The flaw is not in geostatistical theory but rather in

the application, simplistic use of black boxes without

consideration of the underlying phenomenon can lead to

strange results.

It is necessary to incorporate some "expert" knowledge

and/or soft data in such cases.

Donald E. Myers

Department of Mathematics

University of Arizona

Tucson, AZ 85721

http://www.u.arizona.edu/~donaldm
--

*To post a message to the list, send it to

ai-geostats@....

*As a general service to list users, please remember to post a summary

of any useful responses to your questions.

*To unsubscribe, send email to

majordomo@... with no subject and

"unsubscribe ai-geostats" in the message body.

DO NOT SEND Subscribe/Unsubscribe requests to the list!