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摘要翻译：
Kou,Zhou和Wong在最近的一篇论文《等能采样器及其应用统计推断和统计力学》[Ann.Stat.34(2006)1581-1619]中提出了一种新的随机模拟方法--等能采样器。该技术旨在从概率度量$\pi$进行模拟，该度量值可能只知道一个归一化常数。作者证明了采样器在相当具有挑战性的问题中表现良好，但它们的收敛结果（定理2）似乎是不完全的。Atchad\'e&Liu(2006)在讨论中指出了这一点，他提出了一个替代收敛性证明。然而，这个替代的证明，虽然理论上是正确的，但并不符合所实现的算法。本文基于Poisson方程和Andrieu等人的理论，给出了等能量采样器收敛性的一个新的证明。（2007）对于\emph{非线性}马尔可夫链蒙特卡罗(MCMC)。本说明的目的是在只有一个进料链时提供EE取样器正确性的证明；一般情况下需要更多的技术方法，而不适合于一个简短的笔记。此外，我们还试图强调与分析这类算法相关的困难，并提出可能采用的主要技术来证明它的收敛性。
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英文标题：
《A note on convergence of the equi-energy sampler》
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作者：
Christophe Andrieu, Ajay Jasra, Arnaud Doucet and Pierre Del Moral
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最新提交年份：
2007
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分类信息：
一级分类：Statistics 统计学
二级分类：Computation 计算
分类描述：Algorithms, Simulation, Visualization
算法、模拟、可视化
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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：
In a recent paper `The equi-energy sampler with applications statistical inference and statistical mechanics' [Ann. Stat. 34 (2006) 1581--1619], Kou, Zhou & Wong have presented a new stochastic simulation method called the equi-energy (EE) sampler. This technique is designed to simulate from a probability measure $\pi$, perhaps only known up to a normalizing constant. The authors demonstrate that the sampler performs well in quite challenging problems but their convergence results (Theorem 2) appear incomplete. This was pointed out, in the discussion of the paper, by Atchad\'e & Liu (2006) who proposed an alternative convergence proof. However, this alternative proof, whilst theoretically correct, does not correspond to the algorithm that is implemented. In this note we provide a new proof of convergence of the equi-energy sampler based on the Poisson equation and on the theory developed in Andrieu et al. (2007) for \emph{Non-Linear} Markov chain Monte Carlo (MCMC). The objective of this note is to provide a proof of correctness of the EE sampler when there is only one feeding chain; the general case requires a much more technical approach than is suitable for a short note. In addition, we also seek to highlight the difficulties associated with the analysis of this type of algorithm and present the main techniques that may be adopted to prove the convergence of it.
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PDF链接：
https://arxiv.org/pdf/711.0164
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