A multivariate extension of a vector of two-parameter Poisson-Dirichlet processes

Weixuan Zhu and Fabrizio Leisen

Journal of Nonparametric Statistics, 2015, vol. 27, issue 1, 89-105

Abstract: In the big data era there is a growing need to model the main features of large and non-trivial data sets. This paper proposes a Bayesian nonparametric prior for modelling situations where data are divided into different units with different densities, allowing information pooling across the groups. Leisen and Lijoi [(2011), 'Vectors of Poisson-Dirichlet processes', J. Multivariate Anal. , 102, 482-495] introduced a bivariate vector of random probability measures with Poisson-Dirichlet marginals where the dependence is induced through a Lévy's Copula. In this paper the same approach is used for generalising such a vector to the multivariate setting. A first important contribution is the derivation of the Laplace functional transform which is non-trivial in the multivariate setting. The Laplace transform is the basis to derive the exchangeable partition probability function (EPPF) and, as a second contribution, we provide an expression of the EPPF for the multivariate setting. Finally, a novel Markov Chain Monte Carlo algorithm for evaluating the EPPF is introduced and tested. In particular, numerical illustrations of the clustering behaviour of the new prior are provided.

Date: 2015
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DOI: 10.1080/10485252.2014.966103

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