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Bayesian countable representation of some population genetics diffusions (Venue: GH seminar RM2)

Presented by: 
M Ruggiero [Torino]
Tuesday 7th August 2007 - 09:30 to 10:00
INI Seminar Room 2

The Fleming-Viot processes are probability-measure-valued diffusions which arise as large population limits of a wide class of population genetics models. In a few formulations their stationary distribution is known to be either the Dirichlet process or a functional of the Dirichlet process, but the connections with Bayesian statistics are still to be explored. This work provides several explicit constructions of Fleming-Viot processes in the Bayesian nonparametric framework, and yields a previously unknown stationary distribution. In particular, by means of known and newly defined generalised Pòlya-urn schemes, several types of pure jump particle processes are introduced, describing the evolution in time of an exchangeable population. In each case, the process of empirical measures of the individuals converges in the Skorohod space to a specific Fleming-Viot diffusion, and the stationary distribution is the de Finetti measure of the infinite sequence of individuals. In presence of viability selection the stationary distribution turns out to be the two-parameter Poisson-Dirichlet process.

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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons