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Vectors of two-parameter Poisson-Dirichlet processes

Author

Listed:
  • Fabrizio Leisen

    (Universidad Carlos III de Madrid)

  • Antonio Lijoi

    (Department of Economics and Quantitative Methods, University of Pavia, and Collegio Carlo Alberto)

Abstract

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 L´evy 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.

Suggested Citation

  • Fabrizio Leisen & Antonio Lijoi, 2010. "Vectors of two-parameter Poisson-Dirichlet processes," Quaderni di Dipartimento 119, University of Pavia, Department of Economics and Quantitative Methods.
    • Handle: RePEc:pav:wpaper:119
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    References listed on IDEAS

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