Open Access
2014 On the topological support of species sampling priors
Pier Giovanni Bissiri, Andrea Ongaro
Electron. J. Statist. 8(1): 861-882 (2014). DOI: 10.1214/14-EJS912


In Bayesian nonparametric statistics, it is crucial that the support of the prior is very large. Here, we consider species sampling priors. Such priors are widely used within mixture models and it has been shown in the literature that a large support for the mixing prior is essential to ensure the consistency of the posterior. In this paper, simple conditions are given that are necessary and sufficient for the support of a species sampling prior to be full. In particular, for proper species sampling priors, the condition is that the maximum size of the atoms of the corresponding process is small with positive probability. We apply this result to show that the main classes of species sampling priors known in literature have full support under mild conditions. Moreover, we find priors with a very simple construction still having full support.


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Pier Giovanni Bissiri. Andrea Ongaro. "On the topological support of species sampling priors." Electron. J. Statist. 8 (1) 861 - 882, 2014.


Published: 2014
First available in Project Euclid: 26 June 2014

zbMATH: 1348.62102
MathSciNet: MR3229100
Digital Object Identifier: 10.1214/14-EJS912

Primary: 62F15 , 62G99

Keywords: Bayesian nonparametrics , consistency of posteriors , Dirichlet process , species sampling priors , topological support of measures

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.8 • No. 1 • 2014
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