A conditional algorithm for Bayesian finite mixture models via normalized point process
Raffaele Argiento · 2016
Modelling via finite mixtures is one of the most fruitful Bayesian approach, particularly useful when there is unobserved heterogeneity in the data. The most popular algorithm under this model is the reversible jump MCMC, that can be nontrivial to design, especially in high-dimensional spaces. In this work, we first introduce a class of finite discrete random probability measures obtained by normalization of finite point processes. Then, we use the new class as the mixing measure of a mixture model and derive its posterior characterization. The resulting new class encompasses the popular finite Dirichlet mixture model; here, in order to compute posterior, we propose an alternative to the reversible jump. In particular, borrowing notation from the nonparametric Bayesian literature, we set up a conditional MCMC algorithm based on the posterior characterization of the unnormalized point process. In order to show the performance of our algorithm and the flexibility of the model, we illustrate some examples on the popular Galaxy dataset.