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August 2014 Bayesian inference with dependent normalized completely random measures
Antonio Lijoi, Bernardo Nipoti, Igor Prünster
Bernoulli 20(3): 1260-1291 (August 2014). DOI: 10.3150/13-BEJ521

Abstract

The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we introduce a flexible class of dependent nonparametric priors, investigate their properties and derive a suitable sampling scheme which allows their concrete implementation. The proposed class is obtained by normalizing dependent completely random measures, where the dependence arises by virtue of a suitable construction of the Poisson random measures underlying the completely random measures. We first provide general distributional results for the whole class of dependent completely random measures and then we specialize them to two specific priors, which represent the natural candidates for concrete implementation due to their analytic tractability: the bivariate Dirichlet and normalized $\sigma$-stable processes. Our analytical results, and in particular the partially exchangeable partition probability function, form also the basis for the determination of a Markov Chain Monte Carlo algorithm for drawing posterior inferences, which reduces to the well-known Blackwell–MacQueen Pólya urn scheme in the univariate case. Such an algorithm can be used for density estimation and for analyzing the clustering structure of the data and is illustrated through a real two-sample dataset example.

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Antonio Lijoi. Bernardo Nipoti. Igor Prünster. "Bayesian inference with dependent normalized completely random measures." Bernoulli 20 (3) 1260 - 1291, August 2014. https://doi.org/10.3150/13-BEJ521

Information

Published: August 2014
First available in Project Euclid: 11 June 2014

zbMATH: 1309.60048
MathSciNet: MR3217444
Digital Object Identifier: 10.3150/13-BEJ521

Rights: Copyright © 2014 Bernoulli Society for Mathematical Statistics and Probability

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Vol.20 • No. 3 • August 2014
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