- Greetings,

At the risk of deviating from the LMC discussion and extending to a more

general problem, I would like to comment on Todd Mowrer's note and include

the relevance of negative prediction variances in general.

By definition, the loss function for the BLUP used to compute the kriging

weights involves the true variance/covariance structure of the random

field which itself is by definition positive definite. Otherwise it would

not be a true covariance. It's fairly straight-forward to add an nxn bias

matrix and an nx1 bias vector to the covariance matrix and vector used to

directly compute the weights. This shows that if the covariance function

is misspecified then the predictions will be biased as well by a term

involving the bias matrix and vector, true covariance matrix and vector,

and observation vector as well. This may happen for example when a

covariance function is estimated without properly defining the

constraints.

Therefore, what I suggest is that negative prediction variances are more

to be interpreted as symptoms of a greater problem, e.g. that being proper

definition of the true parameter space with respect to the covariance

function where the covariance function itself is the parameter.

I agree the literature is riddled with examples of non-admissible

variograms and covariograms. Zonal anisotropic models are a good example.

But I would submit that simply not having negative prediction variances

does not necessarily get you home free. To say the least, having negative

prediction variances should be cause for concern. The covariance model

itself has to be proven admissible (and of course properly estimated).

L. Scott Baggett

Rice University

Department of Statistics, MS138

6100 Main Street

Houston, TX 77005-1892

On Fri, 4 Jun 1999, Todd Mowrer wrote:

> Let me precede my comment with a clear statement that I would never

> ignore the linear model of coregionalization (LMC) in my analyses.

> However, there are citable instances in the non-theoretical

> subject-matter literature of people apparently ignoring it, and it is

> conceivable that one might be asked to peer review such an article.

> Now for argument's sake, from a "devil's advocate" position, my

> question is: What is the consequence of negative cokriging variances?

> Does one no longer have a best linear unbiased estimator? It would seem

> to me that one would still obtain a minimum variance (from the

> semi-variogram) weighted combination of measured values to estimate

> unknown locations. If you don't use cokriging variances for anything,

> e.g., co-conditional simulation, (or even look at them, much less

> mention them ), why care?

> Now if you can't invert a matrix, you'll know it. And if you get a

> "spikey" response surface for your primary response variable, that's

> obviously not good for predictive purposes. But if you get a

> "reasonable" response surface (particularly one with a lower

> cross-validation score than from a conservative coregionalized model),

> then it would seem one has gotten off free, perhaps by stumbling into a

> set of (cross) variograms that work (conform to the LMC). Thank you for

> your comments to help me understand the LMC better.

> Best regards...

> Todd Mowrer, Research Scientist

> Rocky Mountain Research Station

> USDA Forest Service

> Fort Collins, Colorado 80526 USA

> tmowrer/rmrs@...

> tmowrer@...

> tel: +970 498-1255

> --

> *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!

>

--

*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! - On Fri, 4 Jun 1999, Todd Mowrer wrote:

> question is: What is the consequence of negative cokriging variances?

Hello Todd,

> Does one no longer have a best linear unbiased estimator? It would seem

> to me that one would still obtain a minimum variance (from the

> semi-variogram) weighted combination of measured values to estimate

> unknown locations. If you don't use cokriging variances for anything,

> e.g., co-conditional simulation, (or even look at them, much less

> mention them ), why care?

it seems to me that if you seek a minimum variance estimator, an important

constraint is that your variance MUST be non negative ! In this case, a

null variance would mean exact interpolation, as it is the case when

kriging at a data point (kriging is an exact interpolator). If you allow

negative variance, there is no minimum anymore, or more exactly the

theoretical minimum variance is - infinity !!!!

Now, if you don't care about kriging variances, and don't even look at

them, wht bother with a statistical, probability based, approach ?

Why don't you use any interpolation package ?

The main point of geostatistics, vs mere interpolation is that it provides

a measure of the estimation uncertainty (the kriging variance) along

with the interpolation itself, at the cost of a model -- the variogram(s).

For me, mismodeling the variogram and ignoring the kriging variance is

simply missing the point.

Denis Allard

.------------------------Denis ALLARD--------------------------------.

| Unite de Biometrie allard@... |

| INRA Domaine St Paul, Site Agroparc tel: (33) 4 90 31 62 30 |

| 84914 AVIGNON cedex 9, FRANCE fax: 62 52 |

`--------- http://www.avignon.inra.fr/biometrie/welcome.html --------'

--

*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! - Hello everybody,

I'm novice using GSLIB2, and after taking a quicklook in the User's Guide,

I've missed one capability in gamv.f program. When calculating variogram

gamma(h) (whatever option you choose) it could be interesting to have h

as a non-equally distributed distances array. Unfortunately, it

seems that gamv.f outputs h as an equally-grided one. This is not

important when number of points per lag is high, but not the same when

it's low.

I was wondering if anybody has "patched" this issue by adding some

code lines to gamv.f. Any experiences?

Thanks in advance,

Octavi.

=================================================================

Octavi Fors Aldrich

Astronomy Department

Physics Faculty

Avgda. Diagonal 647

08028 Barcelona

SPAIN

Telf: 34-934021122

Fax: 34-934021133

e-mail: octavi@...

=================================================================

--

*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! - Hi all,

I have some question concerning the modeling.

I have calculated different variogram estimators.

The traditional semivariogram reveals spatial continuity. But the

shape, the ranges and anisotropies are better estimated by the more

robust pairwise relative semivariogram.

My questions are:

(1) Could I model the experimental pairwise relative semivariogram

(or other more robust variograms) or does it affect the

kriging estimator and it's estimation variance considering the

accuracy? And if yes do I have to standardize the sill to one?

(2) Is there a difference between modeling the traditional

semivariogram with it's original sill value and with a sill

standardized to one.

(3) What is really necessary to yield the correct estimates? Only the

ratios of nugget and sill structures and their corresponding ranges

or the real values provided by the traditional semivariogram with a

non standardized sill?

Goovaerts 1997 ("Geostatistics for natural resources estimation")

warns against using the more robust estimators as substitutes for

the traditional semivariogram. But for example Srivastava and Parker

1989 ("Robust measures of spatial continuity") did model several

robust estimators besides the traditional semivariogram.

If a robust measure provides a better spatial continuity I would say

that I can use it for modeling. Only the estimation variance will be

affected and should not be taken as an absolute value but used in

relative terms to compare the variances.

Thanks in advance

Ulrich

><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

Ulrich Leopold

Department of Soil Science

The University of Trier

E-mail: leop6101@...

phone: 0049-(0)651-140764

address: Engelstr.104, 54292 Trier, Germany

--

*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! - Hi.

I'm looking for a simple plug-in or extension for ARC VIEW in order

to calculate some semivariograms for my forest landscape.

ANyone know of any scripts for download etc ?

Thanks,

Mark

--

*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!