A new estimator of the discovery probability

Stafano Favaro (stefano.favaro@unito.it), Antonio Lijoi (lijoi@unipv.it) and Igor Prünster (igor@econ.unito.it)
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Stafano Favaro: University of Turin and Collegio Carlo Alberto
Antonio Lijoi: Department of Economics and Management, University of Pavia and Collegio Carlo Alberto
Igor Prünster: University of Turin and Collegio Carlo Alberto

No 7, DEM Working Papers Series from University of Pavia, Department of Economics and Management

Abstract: Species sampling problems have a long history in ecological and biological studies and a number of issues, including the evaluation of species richness, the design of sampling experiments, the estimation of rare species variety, are to be addressed. Such inferential problems have recently emerged also in genomic applications, however exhibiting some peculiar features that make them more challenging: specifically, one has to deal with very large populations (genomic libraries) containing a huge number of distinct species (genes) and only a small portion of the library has been sampled (sequenced). These aspects motivate the Bayesian nonparametric approach we undertake, since it allows to achieve the degree of flexibility typically needed in this framework. Basing on an observed sample of size n, focus will be on prediction of a key aspect of the outcome from an additional sample of size m, namely the so–called discovery probability. In particular, conditionally on an observed basic sample of size n, we derive a novel estimator of the probability of detecting, at the (n + m + 1)–th observation, species that have been observed with any given frequency in the enlarged sample of size n + m. Such an estimator admits a closed form expression that can be exactly evaluated. The result we obtain allows us to quantify both the rate at which rare species are detected and the achieved sample coverage of abundant species, as m increases. Natural applications are represented by the estimation of the probability of discovering rare genes within genomic libraries and the results are illustrated by means of two Expressed Sequence Tags datasets.

Keywords: Bayesian nonparametrics; Gibbs–type priors; Rare species discovery; Species sampling models; Two–parameter Poisson–Dirichlet process. (search for similar items in EconPapers)
Pages: 28 pages
Date: 2012-10
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (6)

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