[ai-geostats] Typical sample sizes for variogram calculations

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• Greetings, I am coding some basic geostatistical procedures and was curious about the typical sorts of sample sizes researchers run into. I know that sizes
Message 1 of 4 , Nov 3, 2004
Greetings,

I am coding some basic geostatistical procedures and was curious about
the "typical" sorts of sample sizes researchers run into. I know that
sizes of n=1000 are fairly common. How about sizes of N=10,000 or
greater? Are variograms computed on samples this large?

Thanks,

-mark
• The classic example in Isaaks & Srivastava has a lot of data points. More data gives a better description of the process, but the problem is with computation:
Message 2 of 4 , Nov 3, 2004
The classic example in Isaaks & Srivastava has a lot of data points. More
data gives a better description of the process, but the problem is with
computation: 1000 samples gives you 499,500 pairs, whereas 10,000 samples
gives you 49,995,000 pairs. This requires a lot of memory.

Dan

p.s. If you need some basic geostatistical procedures, there are plenty of
programs out there.
____________________________
Dr. Daniel P. Bebber
Department of Plant Sciences
University of Oxford
Oxford
OX1 3RB
Tel. 01865 275060

> -----Original Message-----
> From: Mark Coleman [mailto:mark@...]
> Sent: 03 November 2004 20:40
> To: ai-geostats@...
> Subject: [ai-geostats] Typical sample sizes for variogram calculations
>
>
> Greetings,
>
> I am coding some basic geostatistical procedures and was curious about
> the "typical" sorts of sample sizes researchers run into. I know that
> sizes of n=1000 are fairly common. How about sizes of N=10,000 or
> greater? Are variograms computed on samples this large?
>
> Thanks,
>
> -mark
>
>
>
• Mark, this really depends on how you want to estimate the parameters of the covariance / variogram. If you want to use maximum likelihood, then due to the need
Message 3 of 4 , Nov 4, 2004
Mark,

this really depends on how you want to estimate the parameters of the
covariance / variogram. If you want to use maximum likelihood, then due
to the need to invert a matrix, which is O(n^3), generally sizes above
about 1000 become rather prohibitive on a desktop computer. One possible
alternative that attempts to retain statistical rigour but scale
gracefully with sample size is our Sparse Sequential method:

http://www.ncrg.aston.ac.uk/~csatol/ogp/index.html

Alternatively you could use methods of moment estimators (i.e. the
classic sample variogram) and fit these empirically using some function.
Note that in computing the sample variograms one can work in a
sequential fashion, so that not all pair comparissons need be stored,
but they must be computed .... so it will be slower, scaling as O(n^2)
in the computation of the sample variogram.

cheers

Dan

Mark Coleman wrote:
> Greetings,
>
> I am coding some basic geostatistical procedures and was curious about
> the "typical" sorts of sample sizes researchers run into. I know that
> sizes of n=1000 are fairly common. How about sizes of N=10,000 or
> greater? Are variograms computed on samples this large?
>
> Thanks,
>
> -mark
>
>
>
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--

Dr Dan Cornford d.cornford@...
Computer Science
Aston University
Aston Triangle tel +44 (0)121 204 3451
Birmingham B4 7ET fax +44 (0)121 333 6215

http://www.ncrg.aston.ac.uk/~cornfosd/
• Mark Our free downloadable data sets range from 16 to over 20,000. The biggest set I worked wth was a small section of a South African gold mine - 450,000.
Message 4 of 4 , Nov 4, 2004
Mark