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

We define a new class of random probability measures, approximating the well-known normalized gen- eralized gamma (NGG) process. Our new process is defined from the representation of NGG processes as discrete mea- sures where the weights are obtained by normalization of the jumps of a Poisson process, and the support consists of independent identically distributed location points, how- ever considering only jumps larger than a threshold ?. There- fore, the number of jumps of the new process, called ?-NGG process, is a.s. finite. A prior distribution for ? can be elicited. We assume such a process as the mixing measure in a mix- ture model for density and cluster estimation, and build an efficient Gibbs sampler scheme to simulate from the pos- terior. Finally, we discuss applications and performance of the model to two popular datasets, as well as comparison with competitor algorithms, the slice sampler and a posteri- ori truncation.