IDEAS home Printed from https://ideas.repec.org/p/icr/wpmath/13-2007.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.bemservizi.unito.it/repec/icr/wp2007/ICERwp13-07.pdf
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dawson, Donald A. & Feng, Shui, 1998. "Large deviations for the Fleming-Viot process with neutral mutation and selection," Stochastic Processes and their Applications, Elsevier, vol. 77(2), pages 207-232, September.
    2. Desai, Michael M. & Nicolaisen, Lauren E. & Walczak, Aleksandra M. & Plotkin, Joshua B., 2012. "The structure of allelic diversity in the presence of purifying selection," Theoretical Population Biology, Elsevier, vol. 81(2), pages 144-157.
    3. 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.
    4. Steinrücken, Matthias & Wang, Y.X. Rachel & Song, Yun S., 2013. "An explicit transition density expansion for a multi-allelic Wright–Fisher diffusion with general diploid selection," Theoretical Population Biology, Elsevier, vol. 83(C), pages 1-14.
    5. 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.
    6. Chen, Yu-Ting & Cox, J. Theodore, 2018. "Weak atomic convergence of finite voter models toward Fleming–Viot processes," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2463-2488.
    7. A. Dawson, Donald & Feng, Shui, 2001. "Large deviations for the Fleming-Viot process with neutral mutation and selection, II," Stochastic Processes and their Applications, Elsevier, vol. 92(1), pages 131-162, March.
    8. Feng, Shui, 2009. "Poisson-Dirichlet distribution with small mutation rate," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 2082-2094, June.
    9. Champagnat, Nicolas & Hass, Vincent, 2023. "Existence, uniqueness and ergodicity for the centered Fleming–Viot process," Stochastic Processes and their Applications, Elsevier, vol. 166(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:icr:wpmath:13-2007. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Daniele Pennesi (email available below). General contact details of provider: https://edirc.repec.org/data/icerrit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.