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Bayesian Nonparametric Construction of the Fleming-Viot Process with Fertility Selection

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  • Stephen G. Walker
  • Matteo Ruggiero

Abstract

This paper provides the construction in a Bayesian setting of the Fleming-Viot measurevalued process with diploid fertility selection and highlights new connections between Bayesian nonparametrics and population genetics. Via a generalisation of the Blackwell-MacQueen Polya-urn scheme, a Markov particle process is defined such that the associated process of empirical measures converges to the Fleming-Viot diffusion. The stationary distribution, known from Ethier and Kurtz (1994), is then derived through an application of the Dirichlet process mixture model and shown to be the de Finetti measure of the particle process. The Fleming-Viot process with haploid selection is derived as a special case.

Suggested Citation

  • Stephen G. Walker & Matteo Ruggiero, 2007. "Bayesian Nonparametric Construction of the Fleming-Viot Process with Fertility Selection," ICER Working Papers - Applied Mathematics Series 13-2007, ICER - International Centre for Economic Research.
    • Handle: RePEc:icr:wpmath:13-2007
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    File URL: http://www.bemservizi.unito.it/repec/icr/wp2007/ICERwp13-07.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.
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