Bayesian nonparametric estimators derived from conditional Gibbs structures

TL;DR

This paper develops Bayesian nonparametric estimators based on Gibbs-type structures, providing tools for predicting future outcomes in applications like genomics.

Contribution

It introduces new conditional distributions and estimators for Gibbs-type priors, enhancing prediction capabilities in Bayesian nonparametrics.

Findings

Derived explicit posterior distributions for Gibbs-type priors

Provided estimators for predicting features of additional samples

Applicable to genomic data prediction tasks

Abstract

We consider discrete nonparametric priors which induce Gibbs-type exchangeable random partitions and investigate their posterior behavior in detail. In particular, we deduce conditional distributions and the corresponding Bayesian nonparametric estimators, which can be readily exploited for predicting various features of additional samples. The results provide useful tools for genomic applications where prediction of future outcomes is required.