This paper provides a countable representation for a class of infinite-dimensional diffusions which extends the infinitely-many-neutral-alleles model and is related to the two-parameter Poisson- Dirichlet process. By means of Gibbs sampling procedures, we define a reversible Moran-type population process. The associated process of ranked relative frequencies of types is shown to converge in distribution to the two-parameter family of diffusions, which is stationary and er- godic with respect to the two-parameter Poisson-Dirichlet distribution. The construction provides interpretation for the limiting process in terms of individual dynamics.
Countable representation for infinite-dimensional diffusions derived from the two parameter Poisson-Dirichlet process
RUGGIERO, MATTEO;
2009-01-01
Abstract
This paper provides a countable representation for a class of infinite-dimensional diffusions which extends the infinitely-many-neutral-alleles model and is related to the two-parameter Poisson- Dirichlet process. By means of Gibbs sampling procedures, we define a reversible Moran-type population process. The associated process of ranked relative frequencies of types is shown to converge in distribution to the two-parameter family of diffusions, which is stationary and er- godic with respect to the two-parameter Poisson-Dirichlet distribution. The construction provides interpretation for the limiting process in terms of individual dynamics.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
