Title: Normalized almost sure finite point processes for mixture models
Authors: Raffaele Argiento - University of Torino (Italy) [presenting]
Abstract: Modelling via finite mixtures is one of the most fruitful Bayesian approach, particularly useful for clustering when there is unobserved heterogeneity in the data. The most popular algorithm under this approach is the reversible jump MCMC that can be nontrivial to design, especially in high-dimensional spaces. We will show how nonparametric methods can be transferred into the parametric framework. We first introduce a class of almost sure finite discrete random probability measures obtained by normalization of finite point processes. Then, we use the new class as mixing measure of a mixture model and derive its posterior characterization. The resulting class encompasses the popular finite Dirichlet mixture model. In order to compute posterior statistics, we propose an alternative to the reversible jump: borrowing notation from the nonparametric Bayesian literature, we set up a conditional MCMC algorithm based on the posterior characterization of the unnormalized point process. To discuss the performance of our algorithm and the flexibility of the model, we illustrate some examples on simulated and real data.