Volume 23, 2019
|Page(s)||271 - 309|
|Published online||17 June 2019|
Optimal compromise between incompatible conditional probability distributions, with application to Objective Bayesian Kriging
EDF R&D, Dpt. PRISME,
6 quai Watier,
2 Université Paris Diderot, Laboratoire de Probabilités, Statistique et Modélisation, France.
* Corresponding author: firstname.lastname@example.org
Accepted: 31 October 2018
Models are often defined through conditional rather than joint distributions, but it can be difficult to check whether the conditional distributions are compatible, i.e. whether there exists a joint probability distribution which generates them. When they are compatible, a Gibbs sampler can be used to sample from this joint distribution. When they are not, the Gibbs sampling algorithm may still be applied, resulting in a “pseudo-Gibbs sampler”. We show its stationary probability distribution to be the optimal compromise between the conditional distributions, in the sense that it minimizes a mean squared misfit between them and its own 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.
Mathematics Subject Classification: 62F15 / 62M30 / 60G15
Key words: Incompatibility / conditional distribution / Markov kernel / optimal compromise / Kriging / reference prior / integrated likelihood / Gibbs sampling / posterior propriety / frequentist coverage
© The authors. Published by EDP Sciences, SMAI 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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