Bayesian Inference on Mixtures of Distributions

TL;DR

This survey reviews advanced Bayesian methods for mixture models, including new distribution types, closed-form solutions, and improved Bayes factor computation techniques, enhancing understanding and application in statistical inference.

Contribution

It extends previous work by incorporating multinomial, latent class, and t-distributions, and provides new insights into Bayesian inference and Bayes factor calculations.

Findings

Introduces closed-form solutions for certain discrete mixture models

Examines Bayesian inference for multinomial, latent class, and t-distributions

Provides improved methods for computing Bayes factors

Abstract

This survey covers state-of-the-art Bayesian techniques for the estimation of mixtures. It complements the earlier Marin, Mengersen and Robert (2005) by studying new types of distributions, the multinomial, latent class and t distributions. It also exhibits closed form solutions for Bayesian inference in some discrete setups. Lastly, it sheds a new light on the computation of Bayes factors via the approximation of Chib (1995).