In intrinsic geostatistics, spatial continuity is described by a model

(usually the 'theoretical' variogram). Its parameters are estimated by

fitting the model to the moment-based Matheron non-parametric

('empirical') variogram (with several methods available for estimation).

Despite being estimated, the model variogram is treated as known in

intrinsic geostatistics, i.e. the covariance matrix of variogram

parameters is ignored. The assumedly known (but actually estimated)

model is then used in kriging. I asked then what was the feeling of

people in this list about the effect of model-variogram parameter

uncertainty on kriging, in particular OK.

Ruben

---------------

My original question:

Dear list members:

Do you expect that the uncertainty related to estimating variogram

parameters have a strong effect on spatial prediction via ordinary

kriging? It is my impression that usually the analist disregard this

source of variance and proceeds as if these parameters from the

variogram were known. This might be justified since normally the sample

size (pairs of observations) is quite high when fitting the variogram

via weighted least squares, for instance. Any opinion on this and/or

references would be much welcome.

Thanks

Ruben Roa

---------------

Additional point raised:

Dear list members,

Following Ruben Roa's email, I would like to add that I did not

find any clear criterion to what is the minimum number of data

pairs that should be used in each lag and this would certainly

affect the variogram uncertainty. I know that a minimum of 30 data

pairs is used frequently but my impression is that this is a "rule

of thumb". I guess this rule originated from the central limit

theorem (?). I found that the lack of a clear criterion might have

a big effect on the estimation of the Variogram especially in cases

where the data points are non regular and in cases where a non

parametric variogram might be considered.

I would gratefully appreciate any comments on this as well.

Thanks,

Arie

---------------

Response to point raised by Arie:

I do not know if it is a rule of thumb. But it also depends on the

variability of your data values. I think it is quite subjective how much

pairs you will use.

But you should also consider some more robust variogram estimators as

correlogram

or standardized variograms to see if

there are no artificial structures or erratic structures caused by

extreme

values or outliers or even trends...

There is a paper which is quite interesting:

Srivastava, R.M.; Parker, H.M., 1989:Robust measures of spatial

continuity. In: Armstrong, M., 1989 (editor):Geostatistics. Vol.I.

Dordrecht, pp. 295-308.

Regards, Ulrich

---------------

Response to my original question:

Ruben -

The variogram parameters you select will influence the final model. In

my experience, however, the number of neighboring samples can have a

greater influence than the variogram parameters. I have attached a

paper describing the selection of the number of samples to use when

kriging. This is also described in my book on "Geostatistical Error

Management". You can also visit my website at http://www.gemdqos.com

Jeff Myers

---------------

Response to my original question:

You might want to look at a recent book by M. Stein, Some Theory about

kriging, Springer Publishers

Donald E. Myers

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