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Vectors of two-parameter Poisson-Dirichlet processes

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  • Leisen, Fabrizio
  • Lijoi, Antonio

Abstract

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 [sigma]-stable process. Thus dependence is achieved by applying a Lévy 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

  • Leisen, Fabrizio & Lijoi, Antonio, 2011. "Vectors of two-parameter Poisson-Dirichlet processes," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 482-495, March.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:3:p:482-495
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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.
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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. Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2014. "Beta-product dependent Pitman–Yor processes for Bayesian inference," Journal of Econometrics, Elsevier, vol. 180(1), pages 49-72.
    3. Andrés F. Barrientos & Alejandro Jara & Fernando A. Quintana, 2017. "Fully Nonparametric Regression for Bounded Data Using Dependent Bernstein Polynomials," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 806-825, April.
    4. Burda, Martin & Prokhorov, Artem, 2014. "Copula based factorization in Bayesian multivariate infinite mixture models," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 200-213.
    5. Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2011. "Beta-product Poisson-Dirichlet Processes," DES - Working Papers. Statistics and Econometrics. WS 12160, Universidad Carlos III de Madrid. Departamento de Estadística.
    6. Weixuan Zhu & Fabrizio Leisen, 2015. "A multivariate extension of a vector of two-parameter Poisson-Dirichlet processes," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(1), pages 89-105, March.
    7. Riva Palacio, Alan & Leisen, Fabrizio, 2018. "Integrability conditions for compound random measures," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 32-37.
    8. 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.
    9. 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.
    10. François Caron & Emily B. Fox, 2017. "Sparse graphs using exchangeable random measures," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1295-1366, November.
    11. Riva-Palacio, Alan & Leisen, Fabrizio, 2021. "Compound vectors of subordinators and their associated positive Lévy copulas," Journal of Multivariate Analysis, Elsevier, vol. 183(C).

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