Alpha-diversity processes and normalized inverse-Gaussian diffusions

Ruggiero, Matteo and Walker, Stephen G. and Favaro, Stefano (2013) Alpha-diversity processes and normalized inverse-Gaussian diffusions. Annals of Applied Probability, 23 (1). ISSN 1050-5164. (In press) (The full text of this publication is not available from this repository)

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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
Uncontrolled keywords: Gibbs partitions, Poisson-Dirichlet, generalized gamma, infinitely-many-neutral-alleles model, time-varying mutation rate.
Subjects: Q Science
Q Science > QA Mathematics (inc Computing science)
Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: Stephen Walker
Date Deposited: 03 Oct 2012 21:58
Last Modified: 25 Jun 2014 10:57
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