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One Step Entropy Variation in Sequential Sampling of Species for the Poisson-Dirichlet Process

One Step Entropy Variation in Sequential Sampling of Species for the Poisson-Dirichlet Process 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 Archer et al. (J. Mach. Learn. Res. 15(1):2833–2868, 2014). 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

One Step Entropy Variation in Sequential Sampling of Species for the Poisson-Dirichlet Process

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-023-00558-6
Publisher site
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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 Archer et al. (J. Mach. Learn. Res. 15(1):2833–2868, 2014). 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.

Journal

Acta Applicandae Mathematicae – Springer Journals

Published: Apr 1, 2023

Keywords: Entropy; Bayesian posterior distribution; Poisson-Dirichlet process; New species discovery; 94A17

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