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The Neutral Population Model and Bayesian Nonparametrics

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  • Stefano Favaro

    ()

  • Matteo Ruggiero

    ()

  • Dario Spanò

    ()

  • Stephen G. Walker

    ()

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    Abstract

    In this paper a widely-studied model in Population Genetics, the so-called Infinitely- Many-Alleles model with neutral mutation, is reinterpreted in terms of a timedependent Bayesian nonparametric statistical model, where the prior of the model is described by the Neutral Fleming-Viot process. A natural likelihood process is introduced such that every collection of k observations, at each time point, is essentially a vector of i.i.d. samples from the state of the Fleming-Viot process at that time. The dynamic properties of the particle process induced by such a likelihood are studied. The Moran model is derived as the marginal distribution of a timedependent sample induced by such a choice of prior and likelihood. The derivation of all results relies on the transition density of the Neutral Fleming-Viot process and on a new representation for the Dirichlet process.

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    File URL: http://www.icer.it/docs/wp2007/ICERwp18-07.pdf
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    Bibliographic Info

    Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 18-2007.

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    Length: 14 pages
    Date of creation: Mar 2007
    Date of revision:
    Handle: RePEc:icr:wpmath:18-2007

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    Related research

    Keywords: Fleming-Viot process; particle process; Blackwell-MacQueen urn-scheme; transition function; population genetics.;

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    1. Stephen G. Walker & Matteo Ruggiero, 2007. "Construction and Stationary Distribution of the Fleming-Viot Process with Viability Selection," ICER Working Papers - Applied Mathematics Series 14-2007, ICER - International Centre for Economic Research.
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