Bayesian kriging Instead of estimating the parameters, we put a prior distribution on them, and update the distribution using the data. Model: Matrix with.

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Presentation transcript:

Bayesian kriging Instead of estimating the parameters, we put a prior distribution on them, and update the distribution using the data. Model: Matrix with i,j-element C(s i -s j ;  ) (correlation) measurement error      T (Z(s 1 )...Z(s n )) T

Prior and posterior Prior: Posterior: Predictive distribution: kriging predictor

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)

More priors A prior is assigned to. Defaults to fixed=0, 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

Prior/posterior of 

Variogram estimates mean median mode

Predictive mean

Comparison Ordinary kriging Bayesian kriging

Kriging variances BayesClassical range (52,307) range (170,278)

Introduction to geoR Commands available at the web site. “Official” introduction to geoR is ro.pdf ro.pdf