- Hi all,

A few more references to the Covariance Vs. Semi-

variograme discussion:

To support Semi-variograme: Cressie N.A.C. (1993)

Statistics for spatial data. New York Wiley. ( Page 70-

73) I believe that the original discussion appears in:

Cressie A.C. Noel. and Grondona O. Martin (1992); A

comparison of Variogram Estimation with Covariogram

Estimation, In The art of statistical Science Edited by K.V.

Mardia Jhon pp:191-208, Wiley & Sons Ltd.

Cressie proves that semi- variogram estimation is to be

preferred over covariogram estimation; the main reasons

for that are:

1.In the Kriging process where we estimate the mean of the

process and then predict the random process both the

variogram estimator and covariogram estimator are biased.

However the variogram bias is of smaller order.

2. If our data has trend contamination then it has

"disastrous effect" on attempts to estimate the covariogram

while on the variogram it has a "small upward shift".

There is more to that; check on the book..

To support Covariance: Barry and Pace (1997) "Kriging

with large data sets using sparse matrix techniques"

Communications in statistics simulation and computation

Vol 26 (2) pp 619-629 exploit the sparseness of covariance

matrix - with stationary models we have zeros for points

outside the range - and they were able to dramatically lower

the time and storage cost of kriging.

Since the covariance matrix is a symmetric positive definite

matrix, we can use the Cholesky factorization for its

inversion. If A is n-by-n, the computational complexity of

Cholesky(A) is O(n^3), but the complexity of the

subsequent inversion solutions is only O(n^2).

With Marco's suggestion of Matheron equations it seems

that one can use Cholesky factorization even with semi-

variogram matrix.

Thanks for interesting discussions.

Yaron Felus

The Ohio-State University

http://felus.mps.ohio-state.edu/yf/

--

* To post a message to the list, send it to ai-geostats@...

* As a general service to the users, please remember to post a summary of any useful responses to your questions.

* To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list

* Support to the list is provided at http://www.ai-geostats.org - Pierre Goovaerts wrote:
>

Simple kriging is used in many, if not most of today's most

> Given that SIMPLE kriging is rarely used, we might even

> argue that all this discussion is pointless...

commonly used sequential simulation algorithms.

--

Edzer

--

* To post a message to the list, send it to ai-geostats@...

* As a general service to the users, please remember to post a summary of any useful responses to your questions.

* To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list

* Support to the list is provided at http://www.ai-geostats.org