Overfitting Bayesian Mixture Models with an Unknown Number of Components.

This paper proposes solutions to three issues pertaining to the estimation of finitemixture models with an unknown number of components: the non-identifiabilityinduced by overfitting the number of components, the mixing limitations of standardMarkov Chain Monte Carlo (MCMC) sampling techniques, and the related labelswitching problem.An overfitting approach is used to estimate the number of components in a finitemixture model via a Zmix algorithm. Zmix provides a bridge betweenmultidimensional samplers and test based estimation methods, whereby priors arechosen to encourage extra groups to have weights approaching zero. MCMC samplingis made possible by the implementation of prior parallel tempering, an extension ofparallel tempering. Zmix can accurately estimate the number of components, posteriorparameter estimates and allocation probabilities given a sufficiently large sample size.The results will reflect uncertainty in the final model and will reportthe range ofpossible candidate models and their respective estimated probabilities from a singlerun. Label switching is resolved with a computationally light-weight method, Zswitch,developed for overfitted mixtures by exploiting the intuitiveness ofallocation-basedrelabelling algorithms and the precision of label-invariant loss functions.Four simulation studies are included to illustrate Zmix and Zswitch, as well asthree case studies from the literature. All methods are available aspart of the RpackageZmix(github.com/zoevanhavre/Zmix), which can currently be applied tounivariate Gaussian mixture modelsnonnonouirechercheInternationa