Why do we need and how should we implement Bayesian kriging methods |
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| Authors: | Jürgen Pilz Gunter Spöck |
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| Institution: | 1.Department of Statistics,University of Klagenfurt,Klagenfurt,Austria |
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| Abstract: | The spatial prediction methodology that has become known under the heading of kriging is largely based on the assumptions
that the underlying random field is Gaussian and the covariance function is exactly known. In practical applications, however,
these assumptions will not hold. Beyond Gaussianity of the random field, lognormal kriging, disjunctive kriging, (generalized
linear) model-based kriging and trans-Gaussian kriging have been proposed in the literature. The latter approach makes use
of the Box–Cox-transform of the data. Still, all the alternatives mentioned do not take into account the uncertainty with
respect to the distribution (or transformation) and the estimated covariance function of the data. The Bayesian trans-Gaussian
kriging methodology proposed in the present paper is in the spirit of the “Bayesian bootstrap” idea advocated by Rubin (Ann
Stat 9:130–134, 1981) and avoids the unusual specification of noninformative priors often made in the literature and is entirely based on the
sample distribution of the estimators of the covariance function and of the Box–Cox parameter. After some notes on Bayesian
spatial prediction, noninformative priors and developing our new methodology finally we will present an example illustrating
our pragmatic approach to Bayesian prediction by means of a simulated data set. |
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