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

Ongaro, A., Bissiri, P. (2014). On the topological support of species sampling priors. ELECTRONIC JOURNAL OF STATISTICS, 8(1), 861-882 [10.1214/14-EJS912].

On the topological support of species sampling priors

ONGARO, ANDREA;BISSIRI, PIER GIOVANNI
2014

Abstract

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
Articolo in rivista - Articolo scientifico
Bayesian nonparametrics, consistency of posteriors, Dirichlet process, species sampling priors, topological support of measures
English
861
882
22
Ongaro, A., Bissiri, P. (2014). On the topological support of species sampling priors. ELECTRONIC JOURNAL OF STATISTICS, 8(1), 861-882 [10.1214/14-EJS912].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/52913
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