## [ai-geostats] Regional estimation - block kriging or conditional simulation?

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• Hello, At the moment I am examining methods for estimating the mean and the variance of the mean of irregularly shaped blocks, in this case soil units and
Message 1 of 1 , Mar 15, 2006
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Hello,

At the moment I am examining methods for estimating the mean and the
variance of the mean of irregularly shaped blocks, in this case soil
units and agricultural fields, based on an irregular soil sampling
scheme.

The simplest solution is block kriging based on a fine mesh
discretization of the block. However when the range of the variogram is
less than the lengths of the block being estimated this is not
recommended. In this situation conditional simulation is recommended,
e.g the GSLIB manual and some papers by Goovaerts. This involves
simulating values, conditional to the samples, onto a fine grid covering
the block. Over many realizations, the mean and its variance of the
region may be estimated from the simulated values on the fine grid. In
particular, LU Decompsition has been mentioned.

This issue has been raised on the list a few years ago but it was not
clear which way was best.

Other than getting a pdf, some reasons for preferring simulation
include:
(i) numerical instabilities when block kriging with large matrices
(ii) the semivariogram is most accurate at short lags so to using
modelled semivariance values beyond the range is unwise.

I have used both methods (I used LU Decomposition for simualtion) and
get very similar results which is probably as expected. It seems to me
that problems with block kriging the regional mean equally apply to
conditional simulation when using LU Decomposiiton. LU Decomposiiotn
involves a larger matrix than kriging, and like kriging it uses the
estimates of the semivariance at longer lags to fill out the covariance
matrix between the condtioning data and non-conditioning locations.

I could use other simulation algorithms such as Sequential Gaussian
Simulation but it all seems an overkill when I just want an estimate of
the mean and the variance. Especially if I want to extend my work to
cokrige 4 variables simultaneously, each being equally important. I
imagine this would take a long time with Sequential Gaussian Simulation
let alone the time to code this!

Finally, a good estimate of the variance is equally important as the
mean in my work so finding the mean value based on dividing the blocks
into smaller blocks is not appropriate as it does not give an estimate
of the variance

So given that I just want the mean and variance, and not the pdf, why
should I use simulation, especially using LU Decompsition, when the
results are the same?

Would it be wise to state that if you only want the mean and variance =
use block kriging, if you want a pdf = use condtional simulation?

Tom

Thomas Bishop

Biomathematics and Bioinformatics Division
Rothamsted Research
Harpenden
Hertfordshire
AL5 2JQ
United Kingdom
Tel: + 44 (0) 1582 763 133 ext 2574
Fax: + 44 (0) 1582 760 981
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