Stein’s method for the Poisson–Dirichlet distribution and the Ewens sampling formula, with applications to Wright–Fisher models
Stein’s method for the Poisson–Dirichlet distribution and the Ewens sampling formula, with applications to Wright–Fisher models
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泊松-狄利克雷分布的 Stein 方法和 Ewens 抽样公式，及其在 Wright-Fisher 模型中的应用
DOI：
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Nathan Ross
中科院分区：
文献类型：
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作者：
H. L. Gan;Nathan Ross
我们提供了一个一般性定理的边界误差的近似随机测量的兴趣-例如，在赖特-费舍尔模型的类型的经验人口措施-和狄利克雷过程，这是一个措施具有泊松-狄利克雷分布原子i.i.d.标签从扩散分布。近似定理的隐式度量捕获了质量的大小和位置，因此也产生了感兴趣的测度和泊松-狄利克雷分布的质量之间的近似边界。我们应用的结果来约束的错误的近似的静态分布的类型在有限的Wright-Fisher模型与无限等位基因突变结构（不一定父独立）的Poisson-Dirichlet分布。我们的结果的一个重要后果是一个明确的上限之间的总变化距离的随机分区产生的抽样从有限的赖特-费舍尔平稳分布，和Ewens抽样公式。如果样本量$n$远小于$N^{1/6}\log（N）^{-1/2}$，则界很小，其中$N$是总的总体大小。我们的分析需要一个单独的利益的结果，给出了一个明确的限制有限赖特-费舍尔平稳分布的类型的数量的二阶矩。一般的近似结果来自于Stein方法对Dirichlet过程的新发展，该方法将Dirichlet过程视为Fleming-Viot过程的平稳分布，然后应用Barthel的生成器方法。
We provide a general theorem bounding the error in the approximation of a random measure of interest--for example, the empirical population measure of types in a Wright-Fisher model--and a Dirichlet process, which is a measure having Poisson-Dirichlet distributed atoms with i.i.d. labels from a diffuse distribution. The implicit metric of the approximation theorem captures the sizes and locations of the masses, and so also yields bounds on the approximation between the masses of the measure of interest and the Poisson-Dirichlet distribution. We apply the result to bound the error in the approximation of the stationary distribution of types in the finite Wright-Fisher model with infinite-alleles mutation structure (not necessarily parent independent) by the Poisson-Dirichlet distribution. An important consequence of our result is an explicit upper bound on the total variation distance between the random partition generated by sampling from a finite Wright-Fisher stationary distribution, and the Ewens Sampling Formula. The bound is small if the sample size $n$ is much smaller than $N^{1/6}\log(N)^{-1/2}$, where $N$ is the total population size. Our analysis requires a result of separate interest, giving an explicit bound on the second moment of the number of types of a finite Wright-Fisher stationary distribution. The general approximation result follows from a new development of Stein's method for the Dirichlet process, which follows by viewing the Dirichlet process as the stationary distribution of a Fleming-Viot process, and then applying Barbour's generator approach.
通过 Stein 方法和时间变化进行的扩散近似
DOI：
10.48550/arxiv.1701.07633
发表时间：
2017
期刊：
arXiv e-prints
影响因子：
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作者：
Kasprzak Mikolaj J.
通讯作者：
Kasprzak Mikolaj J.
影响因子：
1.4
作者：
Fu, Yun-Xin
通讯作者：
Fu, Yun-Xin