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The multivariate beta process and an extension of the Polya tree model

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  • Lorenzo Trippa
  • Peter Müller
  • Wesley Johnson

Abstract

We introduce a novel stochastic process that we term the multivariate beta process. The process is defined for modelling-dependent random probabilities and has beta marginal distributions. We use this process to define a probability model for a family of unknown distributions indexed by covariates. The marginal model for each distribution is a Polya tree prior. An important feature of the proposed prior is the easy centring of the nonparametric model around any parametric regression model. We use the model to implement nonparametric inference for survival distributions. The nonparametric model that we introduce can be adopted to extend the support of prior distributions for parametric regression models. Copyright 2011, Oxford University Press.

Suggested Citation

  • Lorenzo Trippa & Peter Müller & Wesley Johnson, 2011. "The multivariate beta process and an extension of the Polya tree model," Biometrika, Biometrika Trust, vol. 98(1), pages 17-34.
    • Handle: RePEc:oup:biomet:v:98:y:2011:i:1:p:17-34
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    File URL: http://hdl.handle.net/10.1093/biomet/asq072
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    Citations

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    Cited by:

    1. Nieto-Barajas, Luis E., 2014. "Bayesian semiparametric analysis of short- and long-term hazard ratios with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 477-490.
    2. 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.
    3. Antonio Lijoi & Bernardo Nipoti, 2014. "A Class of Hazard Rate Mixtures for Combining Survival Data From Different Experiments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 802-814, June.
    4. Igor Prünster & Matteo Ruggiero, 2011. "A Bayesian nonparametric approach to modeling market share dynamics," Carlo Alberto Notebooks 217, Collegio Carlo Alberto.
    5. 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.
    6. Antonio Lijoi & Bernardo Nipoti, 2013. "A class of hazard rate mixtures for combining survival data from different experiments," DEM Working Papers Series 059, University of Pavia, Department of Economics and Management.
    7. Peluso, Stefano & Mira, Antonietta & Muliere, Pietro, 2015. "Reinforced urn processes for credit risk models," Journal of Econometrics, Elsevier, vol. 184(1), pages 1-12.

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