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This paper adopts a Bayesian nonparametric mixture model where the mixingdistribution belongs to the wide class of normalized homogeneous completelyrandom measures. We propose a truncation method for the mixing distribution bydiscarding the weights of the unnormalized measure smaller than a threshold. Weprove convergence in law of our approximation, provide some theoreticalproperties and characterize its posterior distribution so that a blocked Gibbssampler is devised. The versatility of the approximation is illustrated by twodifferent applications. In the first the normalized Bessel random measure,encompassing the Dirichlet process, is introduced; goodness of fit indexes showits good performances as mixing measure for density estimation. The seconddescribes how to incorporate covariates in the support of the normalizedmeasure, leading to a linear dependent model for regression and clustering.

A priori truncation method for posterior sampling from homogeneous normalized completely random measure mixture models