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• ## AI-GEOSTATS: estimation with biased data

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• Dear list members, I am wrestling with particular dilemma regarding how to incorporate data collected without a design or probability basis into kriging
Message 1 of 2 , Mar 27, 2004
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Dear list members,

I am wrestling with particular dilemma regarding how to incorporate data
collected without a design or probability basis into kriging estimators. In
particular I am dealing with data that has clustered and uneven sampling as
well as some bias towards higher data values. Is is appropriate to use
geostatistics to obtain means and variances in this situation. I understand
that the use of biased data was part of the original dilemma and impetus
for the development of geostatistics in the gold mining industry (Cressie,
2003. J Math. Geol. 22:239-252) but I cannot find a satisfactory to the
question of whether you can use biased data in geostatistical estimation.

Based on kriged estimates obtained from biased samples of simulated
spatially autocorrelated data sets with known paramaters, I find that
kriging means are, on average, less biased than the corresponding
arithmetic sample mean. Is this a case where, in practice, the differential
spatial weighting of sample data provided by kriging, results in less
biased means but with little theoretical basis? Secondarily are the
geostatistical variance estimates obtained from biased data theoretically
valid? I guess that you could interpret them in the sense that "if one was
to sample the same random process with the same set of biased sample
locations, the geostatistical variance is the prediction error that one
would observe". The problem lies, I think, in how "representative" the
biased samples are of the random process and, with no design basis to the
sampling, one is left with the inherent logical confound of model-based
estimation methods- that estimates are model-unbiased, provided the model
is correct, but I will never know if the model is correct." So does
geostatistics provide a "better" model for estimation with biased data in
practice in certain situations because of the spatial weighting of samples
or is this theoretically unsound?

I have searched the literature with limited definitive answers but wanted
to engage the group in this discussion and ask for any references on the
subject.

Thanks.

John Walter

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