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November 2017 Sufficientness Postulates for Gibbs-Type Priors and Hierarchical Generalizations
S. Bacallado, M. Battiston, S. Favaro, L. Trippa
Statist. Sci. 32(4): 487-500 (November 2017). DOI: 10.1214/17-STS619

Abstract

A fundamental problem in Bayesian nonparametrics consists of selecting a prior distribution by assuming that the corresponding predictive probabilities obey certain properties. An early discussion of such a problem, although in a parametric framework, dates back to the seminal work by English philosopher W. E. Johnson, who introduced a noteworthy characterization for the predictive probabilities of the symmetric Dirichlet prior distribution. This is typically referred to as Johnson’s “sufficientness” postulate. In this paper, we review some nonparametric generalizations of Johnson’s postulate for a class of nonparametric priors known as species sampling models. In particular, we revisit and discuss the “sufficientness” postulate for the two parameter Poisson–Dirichlet prior within the more general framework of Gibbs-type priors and their hierarchical generalizations.

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S. Bacallado. M. Battiston. S. Favaro. L. Trippa. "Sufficientness Postulates for Gibbs-Type Priors and Hierarchical Generalizations." Statist. Sci. 32 (4) 487 - 500, November 2017. https://doi.org/10.1214/17-STS619

Information

Published: November 2017
First available in Project Euclid: 28 November 2017

zbMATH: 1383.62079
MathSciNet: MR3730518
Digital Object Identifier: 10.1214/17-STS619

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.32 • No. 4 • November 2017
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