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)
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Official URL http://dx.doi.org/10.1214/12-AAP846 |

## 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) |

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