Yet another application of marginals of multivariate Gibbs distributions

TL;DR

This paper demonstrates the utility of marginals of multivariate Gibbs distributions in simplifying Bayesian nonparametric estimators for species sampling, reducing proof complexity in prior work.

Contribution

It provides a simplified approach to deriving Bayesian estimators using Gibbs distribution marginals, improving proof efficiency in species sampling models.

Findings

Simplified derivation of Bayesian estimators

Reduced proof length and complexity

Enhanced understanding of Gibbs distribution applications

Abstract

We give yet another example of the usefulness of working with marginals of multivariate Gibbs distributions (Cerquetti, 2013) in deriving Bayesian nonparametric estimators under Gibbs priors in species sampling problems. Here in particular we substantially reduce length and complexity of the proofs in Bacallado et al. (2013, Th. 1, and Th. 2) for looking backward probabilities under incomplete information.