Statistical Science

Defining Predictive Probability Functions for Species Sampling Models

Jaeyong Lee, Fernando A. Quintana, Peter Müller, and Lorenzo Trippa

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Abstract

We review the class of species sampling models (SSM). In particular, we investigate the relation between the exchangeable partition probability function (EPPF) and the predictive probability function (PPF). It is straightforward to define a PPF from an EPPF, but the converse is not necessarily true. In this paper we introduce the notion of putative PPFs and show novel conditions for a putative PPF to define an EPPF. We show that all possible PPFs in a certain class have to define (unnormalized) probabilities for cluster membership that are linear in cluster size. We give a new necessary and sufficient condition for arbitrary putative PPFs to define an EPPF. Finally, we show posterior inference for a large class of SSMs with a PPF that is not linear in cluster size and discuss a numerical method to derive its PPF.

Article information

Source
Statist. Sci., Volume 28, Number 2 (2013), 209-222.

Dates
First available in Project Euclid: 21 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.ss/1369147912

Digital Object Identifier
doi:10.1214/12-STS407

Mathematical Reviews number (MathSciNet)
MR3112406

Zentralblatt MATH identifier
1331.62152

Keywords
Species sampling prior exchangeable partition probability functions prediction probability functions

Citation

Lee, Jaeyong; Quintana, Fernando A.; Müller, Peter; Trippa, Lorenzo. Defining Predictive Probability Functions for Species Sampling Models. Statist. Sci. 28 (2013), no. 2, 209--222. doi:10.1214/12-STS407. https://projecteuclid.org/euclid.ss/1369147912


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