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Inference for nonconjugate Bayesian Models using the Gibbs sampler
Author(s) -
Carlin Bradley P.,
Polson Nicholas G.
Publication year - 1991
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315430
Subject(s) - gibbs sampling , monte carlo method , mathematics , bayesian probability , a priori and a posteriori , bayesian inference , statistics , humanities , philosophy , epistemology
A Bayesian approach to modeling a rich class of nonconjugate problems is presented. An adaptive Monte Carlo integration technique known as the Gibbs sampler is proposed as a mechanism for implementing a conceptually and computationally simple solution in such a framework. The result is a general strategy for obtaining marginal posterior densities under changing specification of the model error densities and related prior densities. We illustrate the approach in a nonlinear regression setting, comparing the merits of three candidate error distributions.