One step entropy variation in sequential sampling of species for the Poisson-Dirichlet Process

TL;DR

This paper investigates the entropy variation during sequential sampling of species under a Poisson-Dirichlet Process, revealing a monotone functional that indicates new species discovery.

Contribution

It introduces a novel monotone functional based on entropy differences that signals the occurrence of new species in Bayesian species sampling models.

Findings

The functional remains constant only at new species discovery events.

The study provides a theoretical foundation for entropy-based detection of species emergence.

Application to Bayesian nonparametric models enhances species diversity analysis.

Abstract

We consider the sequential sampling of species, where observed samples are classified into the species they belong to. We are particularly interested in studying some quantities describing the sampling process when there is a new species discovery. We assume that the observations and species are organized as a two-parameter Poisson-Dirichlet Process, which is commonly used as a Bayesian prior in the context of entropy estimation, and we use the computation of the mean posterior entropy given a sample developed in [4]. Our main result shows the existence of a monotone functional, constructed from the difference between the maximal entropy and the mean entropy throughout the sampling process. We show that this functional remains constant only when a new species discovery occurs.