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)

Abstract

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:	Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User:	Stephen Walker
Date Deposited:	03 Oct 2012 21:58 UTC
Last Modified:	29 May 2019 09:28 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/31234 (The current URI for this page, for reference purposes)