A New Finite Approximation for the NGG Mixture Model: An Application to Density Estimation

A new class of random probability measures, approximating the well-known normalized generalized gamma (NGG) process, is defined. The new process is built from the representation of NGG processes as discrete measures, where the weights are obtained by normalization of jumps of the Poisson process which are larger than a threshold ε. Consequently, the new process has a finite number of support points a.s. This process is then considered as the mixing measure in a mixture model for density estimation; a blocked Gibbs sampler scheme is also given, to simulate from the posterior. We perform a thorough robustness analysis for the univariate Galaxy dataset and the multivariate Yeast Cell Cycle dataset with respect to the choice of hyperparameters.