COUNTABLE REPRESENTATION FOR INFINITE DIMENSIONAL DIFFUSIONS DERIVED FROM THE TWO-PARAMETER POISSON-DIRICHLET PROCESS
COUNTABLE REPRESENTATION FOR INFINITE DIMENSIONAL DIFFUSIONS DERIVED FROM THE TWO-PARAMETER POISSON-DIRICHLET PROCESS
复制标题
双参数泊松-狄里克雷过程的无限维扩散的可数表示
DOI：
10.1214/ecp.v14-1508
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发表时间：
2009
影响因子：
0.5
通讯作者：
S. Walker
中科院分区：
文献类型：
--
作者：
M. Ruggiero;S. Walker
本文给出了一类无限维扩散的可数表示，它推广了无限多中性等位基因模型，并与两参数Poisson-Dirichlet过程有关.利用Gibbs抽样方法，定义了一个可逆的Moran型人口过程。排序的相对频率的类型相关联的过程中收敛分布的两个参数的家庭的扩散，这是平稳和遍历相对于两个参数的泊松-狄利克雷分布。该结构提供了解释的限制过程中的个人动力学。
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 ergodic with respect to the two-parameter Poisson-Dirichlet distribution. The construction provides interpretation for the limiting process in terms of individual dynamics.