Bayesian density estimation and model selection using nonparametric hierarchical mixtures

We consider mixtures of parametric densities on the positive reals with a normalized generalized gamma process (Brix, 1999) as mixing measure. This class of mixtures encompasses the Dirichlet process mixture (DPM) model, but it is supposedly more flexible in the detection of clusters in the data. With an almost sure approximation of the posterior distribution of the mixing process we can run a Markov chain Monte Carlo algorithm to estimate linear and nonlinear functionals of the predictive distributions. The best-fitting mixing measure is found by minimizing a Bayes factor for parametric against non-parametric alternatives. We illustrate the method with simulated and hystorical data, finding a tradeoff between the best-fitting model and the correct identification of the number of components in the mixture.