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 time-dependent 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 time-dependent 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.

The neutral population model and Bayesian nonparametrics

FAVARO, STEFANO;RUGGIERO, MATTEO;
2007-01-01

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 time-dependent 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 time-dependent 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.
2007
Fleming-Viot process; particle process; Blackwell-MacQueen urn-scheme; transiton function; population genetics
S. Favaro; M. Ruggiero; D. Spanò; S.G. Walker
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/59020
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