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Alpha-diversity processes and normalized inverse-Gaussian diffusions

Ruggiero, Matteo, Walker, Stephen G., Favaro, Stefano (2013) Alpha-diversity processes and normalized inverse-Gaussian diffusions. Annals of Applied Probability, 23 (1). pp. 386-425. ISSN 1050-5164. (doi:10.1214/12-AAP846) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:31234)

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The infinitely-many-neutral-alleles model has recently been extended

to a class of diffusion processes associated with Gibbs partitions

of two-parameter Poisson-Dirichlet type. This paper introduces

a family of infinite-dimensional diffusions associated with a

different subclass of Gibbs partitions, induced by normalized inverse-

Gaussian random probability measures. Such diffusions describe the

evolution of the frequencies of infinitely-many types together with

the dynamics of the time-varying mutation rate, which is driven by

an alpha-diversity diffusion. Constructed as a dynamic version, relative

to this framework, of the corresponding notion for Gibbs partitions,

the latter is explicitly derived from an underlying population model

and shown to coincide, in a special case, with the diffusion approximation

of a critical Galton-Watson branching process. The class of

infinite-dimensional processes is characterized in terms of its infinitesimal

generator on an appropriate domain, and shown to be the limit

in distribution of a certain sequence of Feller diffusions with finitelymany

types. Moreover, a discrete representation is provided by means

of appropriately transformed Moran-type particle processes, where

the particles are samples from a normalized inverse-Gaussian random

probability measure. The relationship between the limit diffusion and

the two-parameter model is also discussed.

Item Type: Article
DOI/Identification number: 10.1214/12-AAP846
Uncontrolled keywords: Gibbs partitions, Poisson-Dirichlet, generalized gamma, infinitely-many-neutral-alleles model, time-varying mutation rate.
Subjects: Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Stephen Walker
Date Deposited: 03 Oct 2012 21:58 UTC
Last Modified: 16 Feb 2021 12:42 UTC
Resource URI: (The current URI for this page, for reference purposes)

University of Kent Author Information

Walker, Stephen G..

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