Bayesian kriging

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Bayesian kriging

• Instead of estimating the parameters, we put a
  prior distribution on them, and update the
  distribution using the data.
• Model

(Z(s1)...Z(sn))T
measurement error
Matrix with i,j-element C(si-sj?) (correlation)
?????????????T
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Prior and posterior

• Prior
• Posterior
• Predictive distribution

kriging predictor
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Specifically

• Exponential isotropic correlation function
• Default correlation model in geoR.
• Prior on ? defaults to flat, but can also be
  normal or fixed
• Prior on ?2 defaults to reciprocal, but can be
  scaled inverse chisquare or flat
• Prior on ? can be exponential, uniform,
  reciprocal, squared reciprocal, or user specified
  (discrete)

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More priors

• A prior is assigned to . Defaults to
  fixed0, but can also be uniform or user
  specified (discrete).
• These choices are made for computational reasons.
  For example, the posterior distribution of ?2 is
  inverse chisquared.
• For details, see
• http//www.leg.ufpr.br/geoR/geoRdoc/bayeskrige.pdf

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Prior/posterior of ?
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Variogram estimates
mean median mode
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Predictive mean
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Comparison
Ordinary kriging Bayesian kriging
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Kriging variances
Bayes
Classical
range (170,278)
range (52,307)
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Introduction to geoR

• Commands available at the web site.
• Official introduction to geoR is
  http//www.leg.ufpr.br/geoR/geoRdoc/vignette/geoRi
  ntro.pdf