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A note on a Bayesian nonparametric estimator of the discovery probability
Annalisa Cerquetti · 2013-04-04 · via math.ST updates on arXiv.org

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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