Vectors of two-parameter Poisson-Dirichlet processes - Fabrizio Leisen; Antonio Lijoi (Università degli Studi di Pavia, Dipartimento di Economia Politica e Metodi Quantitativi (EPMQ), 2010)
The definition of vectors of dependent random probability measures is a topic of interest in applications to Bayesian statistics. They, indeed, 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 s-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.
Keywords: 330; Bayesian nonparametric statistics; Bivariate completely random measures; Levy copula; Partial exchangeability; Poisson-Dirichlet process; Posterior distribution