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Kuo KL, Wang YJ. Analytical Computation of Pseudo-Gibbs Distributions for Dependency Networks. Methodol Comput Appl Probab 2023. [DOI: 10.1007/s11009-023-10016-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/18/2023]
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Petturiti D, Vantaggi B. Probability envelopes and their Dempster-Shafer approximations in statistical matching. Int J Approx Reason 2022. [DOI: 10.1016/j.ijar.2022.08.011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Muré J. Optimal compromise between incompatible conditional probability distributions, with application to Objective Bayesian Kriging. ESAIM-PROBAB STAT 2019. [DOI: 10.1051/ps/2018023] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Abstract
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.
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