A blocked Gibbs sampler for NGG-mixture models via a priori truncation

Abstract We define a new class of random probability\r\nmeasures, approximating the well-known normalized generalized gamma (NGG) process. Our new process is defined\r\nfrom the representation of NGG processes as discrete measures where the weights are obtained by normalization of\r\nthe jumps of Poisson processes and the support consists of\r\nindependent identically distributed location points, however\r\nconsidering only jumps larger than a threshold ε. Therefore, the number of jumps of the new process, called ε-NGG\r\nprocess, is a.s. finite. A prior distribution for ε can be elicited.\r\nWe assume such a process as the mixing measure in a mixture model for density and cluster estimation, and build an\r\nefficient Gibbs sampler scheme to simulate from the posterior. Finally, we discuss applications and performance of\r\nthe model to two popular datasets, as well as comparison\r\nwith competitor algorithms, the slice sampler and a posteriori truncation.