## Electronic Journal of Statistics

- Electron. J. Statist.
- Volume 8, Number 1 (2014), 861-882.

### On the topological support of species sampling priors

Pier Giovanni Bissiri and Andrea Ongaro

#### 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.

#### Article information

**Source**

Electron. J. Statist., Volume 8, Number 1 (2014), 861-882.

**Dates**

First available in Project Euclid: 26 June 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.ejs/1403812155

**Digital Object Identifier**

doi:10.1214/14-EJS912

**Mathematical Reviews number (MathSciNet)**

MR3229100

**Zentralblatt MATH identifier**

1348.62102

**Subjects**

Primary: 62F15: Bayesian inference 62G99: None of the above, but in this section

**Keywords**

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

#### Citation

Bissiri, Pier Giovanni; Ongaro, Andrea. On the topological support of species sampling priors. Electron. J. Statist. 8 (2014), no. 1, 861--882. doi:10.1214/14-EJS912. https://projecteuclid.org/euclid.ejs/1403812155