Optimal compromise between incompatible conditional probability distributions and Objective Bayesian Kriging

Models are often defined through conditional rather than joint distributions, but it is often difficult to check whether the conditional distributions are compatible. When they are not, we give meaning to the intuition that the stationary probability distribution of the associated Pseudo-Gibbs sampler is the optimal compromise between the conditional distributions. This allows us to perform Objective Bayesian analysis of correlation parameters in Kriging models by using univariate conditional Jeffreys-rule posterior distributions instead of the widely used multivariate Jeffreys-rule posterior. This strategy makes the full-Bayesian procedure tractable. Numerical examples show it has near-optimal frequentist performance in terms of prediction interval coverage.