Looking-backward probabilities for Gibbs-type exchangeable random partitions
Abstract
Gibbs-type random probability measures and the exchangeable random partitions they induce represent the subject of a rich and active literature. They provide a probabilistic framework for a wide range of theoretical and applied problems that are typically referred to as species sampling problems. In this paper, we consider the class of looking-backward species sampling problems introduced in Lijoi et al. (Ann. Appl. Probab. 18 (2008) 1519-1547) in Bayesian nonparametrics. Specifically, given some information on the random partition induced by an initial sample from a Gibbs-type random probability measure, we study the conditional distributions of statistics related to the old species, namely those species detected in the initial sample and possibly re-observed in an additional sample. The proposed results contribute to the analysis of conditional properties of Gibbs-type exchangeable random partitions, so far focused mainly on statistics related to those species generated by the additional sample and not already detected in the initial sample.
Cite
@article{arxiv.1504.00828,
title = {Looking-backward probabilities for Gibbs-type exchangeable random partitions},
author = {Sergio Bacallado and Stefano Favaro and Lorenzo Trippa},
journal= {arXiv preprint arXiv:1504.00828},
year = {2015}
}
Comments
Published at http://dx.doi.org/10.3150/13-BEJ559 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)