Title: Non-local priors for mixture models.

Abstract: Choosing the number of components in mixture models remains a central but elusive challenge. Traditional model selection criteria can be either overly liberal or conservative when enforcing parsimony. They may also result in poorly separated components of limited practical use. Non-local priors (NLPs) are a family of distributions that encourage parsimony by enforcing a separation between the models under consideration. We formalize NLPs in the context of mixtures and show how they lead to well-separated components that have non-negligible weight, hence interpretable as distinct subpopulations. We derive tractable expressions and suggest default prior settings aimed at detecting multi-modal densities. We also give a theoretical characterization of the sparsity induced by NLPs and propose easily implementable algorithms to obtain the integrated likelihood and parameter estimates. Although the framework is generic we fully develop the multivariate Normal mixture case based on a novel family of exchangeable moment priors. Our results show a serious lack of sensitivity of the Bayesian information criterion (BIC) and insufficient parsimony of the AIC and local prior counterparts to our formulation.