Exact Bayesian Analysis of Mixtures

TL;DR

This paper demonstrates the feasibility and limitations of performing exact Bayesian analysis on parametric mixture models with exponential family components and conjugate priors, highlighting its practical constraints.

Contribution

It provides a complete Bayesian analysis framework for certain mixture models and discusses the limitations when extending beyond these specific conditions.

Findings

Exact Bayesian analysis is feasible with exponential family components and conjugate priors.

Limitations arise with large sample sizes, non-exponential data, or complex priors.

Highlights the relevance and boundaries of Bayesian methods in mixture models.

Abstract

In this paper, we show how a complete and exact Bayesian analysis of a parametric mixture model is possible in some cases when components of the mixture are taken from exponential families and when conjugate priors are used. This restricted set-up allows us to show the relevance of the Bayesian approach as well as to exhibit the limitations of a complete analysis, namely that it is impossible to conduct this analysis when the sample size is too large, when the data are not from an exponential family, or when priors that are more complex than conjugate priors are used.