A note on a Bayesian nonparametric estimator of the discovery probability

2013/04/03 by Annalisa Cerquetti, Cerquetti, Annalisa
Computer Science · Mathematics · #60G09 #60G58 #Algorithms and Data Compression #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1304.1030

openalex publication_date 2013/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Favaro, Lijoi, and Pruenster (2012, Biometrics, 68, 1188--1196) derive a novel Bayesian nonparametric estimator of the probability of detecting at the (n+m+1)th observation a species already observed with any given frequency in an enlarged sample of size n+m, conditionally on a basic sample of size n. Unfortunately the general result under Gibbs priors (Theorem 2), and consequently the explicit result under (α, θ) Poisson-Dirichlet priors (Proposition 3), appear to be wrong. Here we provide the correct formulas for both the results, obtained by means of a new technique devised in Cerquetti (2013). We verify the correctness of our derivation by an explicit counterproof for the two-parameter Poisson-Dirichlet case.

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