Mixture models applied to heterogeneous populations

TL;DR

This paper evaluates the effectiveness of Bayesian mixture models, particularly Reversible Jump MCMC, in analyzing heterogeneous populations with unknown subpopulations, through simulations and real data application.

Contribution

It assesses the performance of normal mixture models under various heterogeneity levels and prior information, including estimating the number of components.

Findings

Model performance improves with increased heterogeneity.

Reversible Jump MCMC effectively estimates the number of mixture components.

Bayesian methods handle heterogeneity and label-switching issues in mixture models.

Abstract

Mixture models provide a flexible representation of heterogeneity in a finite number of latent classes. From the Bayesian point of view, Markov Chain Monte Carlo methods provide a way to draw inferences from these models. In particular, when the number of subpopulations is considered unknown, more sophisticated methods are required to perform Bayesian analysis. The Reversible Jump Markov Chain Monte Carlo is an alternative method for computing the posterior distribution by simulation in this case. Some problems associated with the Bayesian analysis of these class of models are frequent, such as the so-called "label-switching" problem. However, as the level of heterogeneity in the population increases, these problems are expected to become less frequent and the model's performance to improve. Thus, the aim of this work is to evaluate the normal mixture model fit using simulated data under different settings of heterogeneity and prior information about the mixture proportions. A simulation study is also presented to evaluate the model's performance considering the number of components known and estimating it. Finally, the model is applied to a censored real dataset containing antibody levels of Cytomegalovirus in individuals.