Bayesian Modelling and Inference on Mixtures of Distributions

Abstract

Publisher Summary Mixture distributions comprise a finite or infinite number of components, possibly of different distributional types, that can describe different features of data. The Bayesian paradigm allows for probability statements to be made directly about the unknown parameters, prior or expert opinion to be included in the analysis, and hierarchical descriptions of both local-scale and global features of the model. This chapter aims to introduce the prior modeling, estimation, and evaluation of mixture distributions in a Bayesian paradigm. The chapter shows that mixture distributions provide a flexible, parametric framework for statistical modeling and analysis. Focus is on the methods rather than advanced examples, in the hope that an understanding of the practical aspects of such modeling can be carried into many disciplines. It also points out the fundamental difficulty in doing inference with such objects, along with a discussion about prior modeling, which is more restrictive than usual, and the constructions of estimators, which also is more involved than the standard posterior mean solution. Finally, this chapter gives some pointers to the related models and problems like mixtures of regressions and hidden Markov models as well as Dirichlet priors.