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Biometrika 1998 85(1):73-87; doi:10.1093/biomet/85.1.73
© 1998 by Biometrika Trust
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Monte Carlo methods for Bayesian analysis of constrained parameter problems

MING-HUI CHEN and QI-MAN SHAO

Department of Mathematical Sciences, Worcester Polytechnic Institute 100 Institute Road, Worcester, Massachusetts 01609, U.S.A. mhchen{at}wpi.edu
Department of Mathematics, University of Oregon Eugene, Oregon 97404, U.S.A. qmshao{at}darkwing.uoregon.edu

Constraints on the parameters in a Bayesian hierarchical model typically make Bayesian computation and analysis complicated. Posterior densities that contain analytically intractable integrals as normalising constants depending on the hyperparameters often make implementation of Gibbs sampling or the Metropolis algorithms difficult. By using reweighting mixtures (Geyer, 1995), we develop alternative simulation-based methods to determine properties of the desired Bayesian posterior distribution. Necessary theory and two illustrative examples are provided.

Key Words: Bayesian computation • Bayesian hierarchical model • Gibb sampling • Marginal posterior density estimation


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