Vectors of two-parameter Poisson-Dirichlet processes

JOURNAL OF MULTIVARIATE ANALYSIS

卷:102

Article

Leisen, Fabrizio²  Lijoi, Antonio^1,3,4 

[1] Univ Pavia, Dipartimento Econ Polit & Metodi Quantitat, I-27100 Pavia, Italy

[2] Univ Carlos III Madrid, Dept Estadist, E-28903 Getafe, Madrid, Spain

[3] Coll Carlo Alberto, I-10024 Moncalieri, Italy

[4] CNR IMATI, I-20133 Milan, Italy

关键词: Bayesian nonparametric statistics;    Bivariate completely random measures;    Levy copula;    Partial exchangeability;    Poisson-Dirichlet process;    Posterior distribution;   

DOI  :  10.1016/j.jmva.2010.10.008

来源: Elsevier

【 摘 要 】

The definition of vectors of dependent random probability measures is a topic of interest in applications to Bayesian statistics. They represent dependent nonparametric prior distributions that are useful for modelling observables for which specific covariate values are known. In this paper we propose a vector of two-parameter Poisson-Dirichlet processes. It is well-known that each component can be obtained by resorting to a change of measure of a a-stable process. Thus dependence is achieved by applying a Levy copula to the marginal intensities. In a two-sample problem, we determine the corresponding partition probability function which turns out to be partially exchangeable. Moreover, we evaluate predictive and posterior distributions. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free