Testing for Mixtures: A Bayesian Entropic Approach
Kerrie Lee Mengersen, Christian P. Robert · 1996
Abstract The determination of the number of components in a mixture of parametrised distributions has important bearing in homogeneity testing, cluster analysis and mixture modelling, among other applications. In this paper, we focus on a two-component gaussian model and a test for the presence of a mixture. The proposed test is based on an indifference zone representation of the null hypothesis defined by the Kullback-Leibler distance, and a derivation of the posterior probability that this distance is less than a given threshold using the Gibbs sampler. Due to a new parametrisation of the mixture model, estimation performances are markedly improved, while the Bayesian prior input is reduced to the specification of a single scale parameter. Moreover, the determination of this scale parameter is equivalent to the choice of the above threshold. We illustrate our approach with a Monte Carlo study.