title: The multivariate beta process and an extension of the Polya tree model.
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.
authors: Department of Biostatistics and Computational Biology, Dana-Farber Cancer Institute, Boston, Massachusetts 02115, U.S.A. , ltrippa@jimmy.harvard.edu.
authors: Lorenzo
authors: L
authors: Trippa
authors: Peter
authors: P
authors: Müller
authors: Wesley
authors: W
authors: Johnson
keywords: Dependent random probability measures; Multivariate beta process; Polya tree distribution
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