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Biometrika Advance Access originally published online on November 19, 2007
Biometrika 2007 94(4):769-786; doi:10.1093/biomet/asm061
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© 2007 Biometrika Trust

Articles

Bayesian Nonparametric Estimation of the Probability of Discovering New Species

Antonio Lijoi

Dipartimento di Economia Politica e Metodi Quantitativi, Università degli Studi di Pavia, 27100 Pavia, Italy lijoi{at}unipv.it

Ramsés H. Mena

Departamento de Probabilidad y Estadística, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, México, 04510 México D.F., Mexico ramses{at}sigma.iimas.unam.mx

Igor Prünster

Dipartimento di Statistica e Matematica Applicata, Università degli Studi di Torino, 10122 Torino, Italy igor{at}econ.unito.it

Received for publication 1 June 2006. Revision received 1 February 2007.
  Abstract

We consider the problem of evaluating the probability of discovering a certain number of new species in a new sample of population units, conditional on the number of species recorded in a basic sample. We use a Bayesian nonparametric approach. The different species proportions are assumed to be random and the observations from the population exchangeable. We provide a Bayesian estimator, under quadratic loss, for the probability of discovering new species which can be compared with well-known frequentist estimators. The results we obtain are illustrated through a numerical example and an application to a genomic dataset concerning the discovery of new genes by sequencing additional single-read sequences of cdna fragments.

Key Words: Bayesian nonparametrics • Gibbs-type random partition • Posterior probability of discovering a new species • Sample coverage • Species sampling


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