Monte Carlo Methods for Constrained Parameter Problems

Abstract

Constraints on the parameters in Bayesian hierarchical models typically make Bayesian computation and analysis complicated. Posterior densities that contain analytically intractable integrals as normalizing constants that depend on the hyperparameters often lead to implementation of Gibbs sampling or Metropolis-Hastings algorithms difficult. In this chapter, we use simulation-based methods via the “reweighting mixtures” of Geyer (1994) to compute posterior quantities of the desired Bayesian posterior distribution.