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A multivariate extension of a vector of Poisson- Dirichlet processes

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  • Zhu, Weixuan
  • Leisen, Fabrizio

Abstract

Recently, Leisen and Lijoi (2011) 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 generalizing such a vector to the multivariate setting. Some non-trivial results are proved in the multidimensional case, in particular, the Laplace transform and the Exchangeable Partition Probability function (EPPF). Finally, some numerical illustrations of the EPPF are provided

Suggested Citation

  • Zhu, Weixuan & Leisen, Fabrizio, 2013. "A multivariate extension of a vector of Poisson- Dirichlet processes," DES - Working Papers. Statistics and Econometrics. WS ws132220, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws132220
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    References listed on IDEAS

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    1. De Iorio, Maria & Muller, Peter & Rosner, Gary L. & MacEachern, Steven N., 2004. "An ANOVA Model for Dependent Random Measures," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 205-215, January.
    2. Hatjispyros, Spyridon J. & Nicoleris, Theodoros & Walker, Stephen G., 2011. "Dependent mixtures of Dirichlet processes," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2011-2025, June.
    3. Antonio Lijoi & Ramsés H. Mena & Igor Prünster, 2007. "Controlling the reinforcement in Bayesian non‐parametric mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 715-740, September.
    4. Leisen, Fabrizio & Lijoi, Antonio, 2011. "Vectors of two-parameter Poisson-Dirichlet processes," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 482-495, March.
    5. Kallsen, Jan & Tankov, Peter, 2006. "Characterization of dependence of multidimensional Lévy processes using Lévy copulas," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1551-1572, August.
    6. Griffin, J.E. & Steel, M.F.J., 2006. "Order-Based Dependent Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 179-194, March.
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    Cited by:

    1. Jim E. Griffin & Fabrizio Leisen, 2017. "Compound random measures and their use in Bayesian non-parametrics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 525-545, March.
    2. Riva Palacio, Alan & Leisen, Fabrizio, 2018. "Integrability conditions for compound random measures," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 32-37.
    3. Vladimir Panov, 2017. "Series Representations for Multivariate Time-Changed Lévy Models," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 97-119, March.

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