Sufficientness postulates for Gibbs-type priors and hierarchical generalizations
Institute of Mathematical Statistics
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Bacallado de Lara, S., Battiston, M., Favaro, S., & Trippa, L. (2017). Sufficientness postulates for Gibbs-type priors and hierarchical generalizations. Statistical Science, 32 (4), 487-500. https://doi.org/10.1214/17-STS619
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.
Bayesian nonparametrics, Dirichlet and two parameter Poisson–Dirichlet process, discovery probability, Gibbs-type species sampling models, hierarchical species sampling models, Johnson’s “sufficientness” postulate, Pólya-like urn scheme
Is supplemented by: https://doi.org/10.1214/17-STS619SUPP
. Stefano Favaro is supported by the European Research Council through StG N-BNP 306406. Marco Battiston’s research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) ERC grant agreement number 617071.
External DOI: https://doi.org/10.1214/17-STS619
This record's URL: https://www.repository.cam.ac.uk/handle/1810/270479