Open Access
May 2013 Defining Predictive Probability Functions for Species Sampling Models
Jaeyong Lee, Fernando A. Quintana, Peter Müller, Lorenzo Trippa
Statist. Sci. 28(2): 209-222 (May 2013). DOI: 10.1214/12-STS407


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.


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Jaeyong Lee. Fernando A. Quintana. Peter Müller. Lorenzo Trippa. "Defining Predictive Probability Functions for Species Sampling Models." Statist. Sci. 28 (2) 209 - 222, May 2013.


Published: May 2013
First available in Project Euclid: 21 May 2013

zbMATH: 1331.62152
MathSciNet: MR3112406
Digital Object Identifier: 10.1214/12-STS407

Keywords: exchangeable partition probability functions , prediction probability functions , Species sampling prior

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.28 • No. 2 • May 2013
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