Bayesian mixture modeling using a mixture of finite mixtures with normalized inverse Gaussian weights

In Bayesian inference for mixture models with an unknown number of components, a finite mixture model is usually employed that assumes prior distributions for mixing weights and the number of components. This model is called a mixture of finite mixtures (MFM). As a prior distribution for the weights, a (symmetric) Dirichlet distribution is widely used for conjugacy and computational simplicity, while the selection of the concentration parameter influences posterior inference. As a robust alternative to Dirichlet weights, we present a method based on a MFM with normalized inverse Gaussian weights. The motivation is similar to the use of normalized inverse Gaussian processes instead of Dirichlet processes in nonparametric Bayesian statistics. Introducing latent variables, the posterior computation is carried out using blocked Gibbs sampling without using the reversible jump algorithm. We also consider extensions to dynamic MFMs after clarifying the relationship with telescoping sampling. The performance of the proposed method is illustrated through some numerical experiments and real data examples, including clustering, density estimation, and community detection. Supplementary materials for this article are available online.