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A new estimator of the discovery probability

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  • Stefano 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)

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    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.

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    File URL: http://economia.unipv.it/docs/dipeco/quad/ps/RePEc/pav/demwpp/DEMWP0007.pdf
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    Bibliographic Info

    Paper provided by University of Pavia, Department of Economics and Management in its series DEM Working Papers Series with number 007.

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    Length: 28 pages
    Date of creation: Oct 2012
    Date of revision:
    Handle: RePEc:pav:demwpp:demwp0007

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    Related research

    Keywords: Bayesian nonparametrics; Gibbs–type priors; Rare species discovery; Species sampling models; Two–parameter Poisson–Dirichlet process.;

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    References

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    1. Antonio Lijoi & Ramsés H. Mena & Igor Prünster, 2007. "A Bayesian Nonparametric Method for Prediction in EST Analysis," ICER Working Papers - Applied Mathematics Series 16-2007, ICER - International Centre for Economic Research.
    2. Alejandro Jara & Timothy Hanson & Fernando A. Quintana & Peter Müller & Gary L. Rosner, . "DPpackage: Bayesian Semi- and Nonparametric Modeling in R," Journal of Statistical Software, American Statistical Association, vol. 40(i05).
    3. Kolossiatis, M. & Griffin, J.E. & Steel, M.F.J., 2011. "Modeling overdispersion with the normalized tempered stable distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2288-2301, July.
    4. Antonio Lijoi & Igor Pruenster & Stephen G. Walker, 2008. "Bayesian nonparametric estimators derived from conditional Gibbs structures," ICER Working Papers - Applied Mathematics Series 06-2008, ICER - International Centre for Economic Research.
    5. Chang Xuan Mao, 2002. "A Poisson model for the coverage problem with a genomic application," Biometrika, Biometrika Trust, vol. 89(3), pages 669-682, August.
    6. Antonio Lijoi & Ramsés H. Mena & Igor Prünster, 2007. "Bayesian Nonparametric Estimation of the Probability of Discovering New Species," Biometrika, Biometrika Trust, vol. 94(4), pages 769-786.
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