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AI-GEOSTATS: estimation with biased data

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  • john walter
    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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