Bayesian Inference: Modeling and Computation

Abstract

This chapter explores several practical issues for a Bayesian approach to inference. The first section explores an approach used to specify prior distributions called hierarchical modeling, based on hyperparameters and conditioning. Section 15.2 discusses the robustness to the choice of prior distribution. Sections 15.4 and 15.5 deal with the Metropolis–Hastings algorithm and the Gibbs sampler, simulation methods that can be used to approximate posterior expectations numerically. As background, Section 15.3 provides a brief introduction to Markov chains. Finally, Section 15.6 illustrates how Gibbs sampling can be used in a Bayesian approach to image processing.