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.