Clara Grazian (UNSW, School of Mathematics and Statistics)
Title: The importance of being conservative: Bayesian analysis for mixture modelsAbstract
From a Bayesian perspective, mixture models have been characterised by a restrictive prior modelling, since their ill-defined nature makes most of the improper priors not acceptable. In particular, recent results have shown the inconsistency of the posterior distribution on the number of components when using standard nonparametric prior processes. We propose an analysis of prior choices associated by their property of conservativeness in the number of components. Among the proposals, we derive a prior distribution on the number of clusters which considers the loss one would incur if the true value representing the number of components were not considered. The prior has an elegant and easy to implement structure, which allows to naturally include any prior information one may have as well as to opt for a default solution in cases where this information is not available. The methods are then applied on two real data-sets. The first data-set consists of retrieval times for monitoring IP packets in computer network systems. The second data-set consists of measures registered in antimicrobial susceptibility tests for 14 compounds used in the treatment of M. Tuberculosis. In both the situations, the number of clusters is uncertain and different solutions lead to different interpretations.