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摘要翻译：
考虑一个参数统计模型$p(\mathrm{d}x\theta)$和一个不适当的先验分布$\nu(\mathrm{d}\theta)$一起产生一个（适当的）形式后验分布$q(\mathrm{d}\thetax)$。如果在平方误差损失下，每个有界函数的广义Bayes估计是可容许的，则称先验为强可容许的。Eaton[Ann.Statist.20(1992)1147--1179]证明了$\nu$强可容许的一个充分条件是转移函数为$r(\theta,\mathrm{d}\eta)=\int Q(\mathrm{d}\etax)P(\mathrm{d}x\theta)$的马尔可夫链的局部递归。当与$R$相关的马尔可夫链不可约时，这一结果及其推广的应用往往大大简化。然而，建立不可还原性可能是困难的。本文给出了一般状态空间马氏链不可约性的一个刻划，并利用这个刻划给出了Eaton马氏链不可约性的一个易检验的充要条件。检查此条件所需的只是简单地检查$p$和$\nu$。通过两个算例说明了主要结果的应用。
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英文标题：
《When is Eaton's Markov chain irreducible?》
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作者：
James P. Hobert, Aixin Tan, Ruitao Liu
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
Consider a parametric statistical model $P(\mathrm{d}x|\theta)$ and an improper prior distribution $\nu(\mathrm{d}\theta)$ that together yield a (proper) formal posterior distribution $Q(\mathrm{d}\theta|x)$. The prior is called strongly admissible if the generalized Bayes estimator of every bounded function of $\theta$ is admissible under squared error loss. Eaton [Ann. Statist. 20 (1992) 1147--1179] has shown that a sufficient condition for strong admissibility of $\nu$ is the local recurrence of the Markov chain whose transition function is $R(\theta,\mathrm{d}\eta)=\int Q(\mathrm{d}\eta|x)P(\mathrm {d}x|\theta)$. Applications of this result and its extensions are often greatly simplified when the Markov chain associated with $R$ is irreducible. However, establishing irreducibility can be difficult. In this paper, we provide a characterization of irreducibility for general state space Markov chains and use this characterization to develop an easily checked, necessary and sufficient condition for irreducibility of Eaton's Markov chain. All that is required to check this condition is a simple examination of $P$ and $\nu$. Application of the main result is illustrated using two examples.
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PDF链接：
https://arxiv.org/pdf/709.0448
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