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The Neutral Population Model and Bayesian Nonparametrics

Author

Listed:
  • Stefano Favaro
  • Matteo Ruggiero
  • Dario Spanò
  • Stephen G. Walker

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.

Suggested Citation

  • Stefano Favaro & Matteo Ruggiero & Dario Spanò & Stephen G. Walker, 2007. "The Neutral Population Model and Bayesian Nonparametrics," ICER Working Papers - Applied Mathematics Series 18-2007, ICER - International Centre for Economic Research.
    • Handle: RePEc:icr:wpmath:18-2007
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    File URL: http://www.bemservizi.unito.it/repec/icr/wp2007/ICERwp18-07.pdf
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    References listed on IDEAS

    as
    1. Ethier, S. N. & Kurtz, Thomas G., 1994. "Convergence to Fleming-Viot processes in the weak atomic topology," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 1-27, November.
    2. 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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