- Hi Ulrich

I'm surprised we got mainly "pragmatic" answers to your question and

would have expected from statisticians and mathematicians more reactions

about a possible statistical heresy: the semivariogram model is fitted to an

experimental semivariogram which was obtained from a certain number of points.

To be mathematically correct in terms of the various hypotheses used, should

one not use a search neighbourhood that is equal to the one used to obtain the

semivariogram (frequently all points) ?

If one tries to obtain maps that are "realistic", I mean here maps created by

experts that have some additional knowledge about the investigated phenomenon,

one would most probably try to get rid of various problems that can be solved

by reducing the search radius or the number of neighbours . Pierre's reference

to the impact of the relative nugget effect on points that are located far

away is often a decisive one.

On the other hand, if the main objective is to compare various algorithms

(e.g. ordinary kriging versus indicator kriging, or indicator kriging versus

log-kriging) or kriging variances obtained by various models, I would imagine

that using a "no search" approach (all neighbours are used) would be the most

reasonable approach...

Just a few thoughts.

Gregoire

Ulrich Leopold <uleopold@...> wrote:> Dear list,

any useful responses to your questions.

>

> What would you consider the most reliable ordinary kriging estimate? To

> use a local search neighbourhood (slightly bigger than the effective

> range) or set to global to include *all* data locations?

>

>

> Ulrich

>

>

> --

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> Ulrich Leopold MSc.

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> Phone: +31-(0)20-525-7456 (7451 Secretary)

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* Support to the list is provided at http://www.ai-geostats.org - On Wed, 2003-07-09 at 10:06, Gregoire Dubois wrote:

> I'm surprised we got mainly "pragmatic" answers to your question and

I agree. But then you need to model the experimental semivariogram for

> would have expected from statisticians and mathematicians more reactions

> about a possible statistical heresy: the semivariogram model is fitted to an

> experimental semivariogram which was obtained from a certain number of points.

> To be mathematically correct in terms of the various hypotheses used, should

> one not use a search neighbourhood that is equal to the one used to obtain the

> semivariogram (frequently all points) ?

all distances. Wouldn't this be a problem to find a reliable model fit?

> On the other hand, if the main objective is to compare various algorithms

The objective is to compare different algorithms AND create a most

> (e.g. ordinary kriging versus indicator kriging, or indicator kriging versus

> log-kriging) or kriging variances obtained by various models, I would imagine

> that using a "no search" approach (all neighbours are used) would be the most

> reasonable approach...

realistic map at the same time by using these algorithms. So I guess

there have to made some compromises. Probably cross-validation could

help if I use a sub set of the data set.

Ulrich

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

have expected from statisticians and mathematicians more reactions about a

>

>I'm surprised we got mainly "pragmatic" answers to your question and would

possible statistical heresy: the semivariogram model is fitted to an

experimental semivariogram which was obtained from a certain number of

points. To be mathematically correct in terms of the various hypotheses

used, should one not use a search neighbourhood that is equal to the one

used to obtain the semivariogram (frequently all points) ?

Okay, as a statistician i would say that the use of a restricted

neighbourhood search in kriging is akin to the statistical concept of

'conditioning on a relevant subset'. This concept normally refers to a

relevant subset in the sample space (i.e. all possible samples not just the

actually observed one) while in this case it refers to a relevant subset in

the observed sample given the fitted model. Probably then, an extension of

the concept of relevant subset in the sample space to the case of the

observed sample given a model would justify, from a statistical point of

view, not to use all points in kriging. This seems reasonable too if we

consider the model as taking the place of the sample space, i.e. as the

mechanism generating the samples, which in turns seems consistent with the

general idea of conditioning on an ancillary statistics (the ancillary here

would be the spatial neighbourhood since these neighbourhood does not

depend on the parameter to be estimated, namely the density of the random

variable in the point being interpolated). This is off the top of my head,

so please 'hande with care'.

Ruben

http://webmail.udec.cl

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* Support to the list is provided at http://www.ai-geostats.org- Maybe it is worth pointing out that Ordinary Kriging

with a 'global neighbourhood' (using all the points in

simple speak) is the same as Simple Kriging with a

neighbourhood which extends to the range of influence

of the semi-variogram model (if any).

Given this fact, you would be computationally safer to

do Simple Kriging - otherwise known as "kriging with

known mean" and saving yourself the problems of

enormous and sparse matrix solutions.

The only overhead to Simple Kriging is producing a

reliable estimate of the global mean and, to be

realistic, a standard error associated with it.

Isobel Clark

http://geoecosse.bizland.com/courses.htm

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