Alpha-diversity processes and normalized inverse-Gaussian diffusions.
Alpha-diversity processes and normalized inverse-Gaussian diffusions.
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阿尔法多样性过程和归一化逆高斯扩散。
DOI：
10.1214/12-aap846
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发表时间：
2013
影响因子：
1.8
通讯作者：
S. Favaro
中科院分区：
文献类型：
--
作者：
M. Ruggiero;S. Walker;S. Favaro
无限多中性等位基因模型最近得到了扩展
一类与Gibbs划分有关的扩散过程
两参数Poisson-Dirichlet型介绍
一个家庭的无限维扩散与一个
吉布斯划分的不同子类，由归一化逆-
高斯随机概率测度。这种扩散描述了
无限多类型的频率的演变，
随时间变化的突变率的动态，这是由
α多样性扩散。构造为动态版本，相对
对于这个框架，吉布斯划分的相应概念，
后者显然是从一个基本的人口模型中推导出来的
并在特殊情况下与扩散近似相吻合
一个临界的高尔顿-沃森分支过程。的类
无穷维过程的特征在于它的无穷小
生成器在适当的域，并显示为限制
一类有限多Feller扩散序列的分布
类型此外，通过以下方式提供离散表示：
适当变换的Moran型粒子过程，其中
粒子是来自归一化的逆高斯随机
概率测度极限扩散与
并对双参数模型进行了讨论。
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.
DOI：
10.48550/arxiv.0712.0556
发表时间：
2007
期刊：
--
影响因子：
--
作者：
Goldschmidt C
通讯作者：
Goldschmidt C