Output Analysis for Markov Chain Monte Carlo

与经典的蒙特卡罗方法相比，马尔可夫链蒙特卡罗(MCMC)方法有几个缺点。特别是，每个从业者在实施MCMC时面临的一个重要问题是何时停止计算。通常，会采用经验和特殊方法相结合的方法来做出这一决定。因此，人们不得不怀疑这一推论的质量。研究人员研究顺序固定宽度方法，这些方法允许构建感兴趣数量的区间估计器。区间估计器描述了点估计的置信度。研究人员利用这一点研究了当MCMC计算的目的是估计目标分布的概念量时，有效停止规则的发展，这些方法要求马尔可夫链以几何速度收敛，这反过来意味着在感兴趣的环境中存在点估计的极限分布。因此，研究人员研究了在两大类贝叶斯模型中遇到的马尔可夫链的收敛速度。MCMC方法已经成为应用统计学家(以及许多其他学科的科学家)工具箱中的标准技术。事实上，可以毫不夸张地说，它给应用统计学带来了革命性的变化，特别是贝叶斯分类。不幸的是，MCMC方法并不总是被谨慎地使用，导致了文献中可疑的说法。特别是，在推论结论中纳入不确定性指标的努力寥寥无几。通过向统计学家和其他科学家提供使用MCMC在他们的研究环境中进行推理的有效技术，严格解决根据这些不确定性衡量的停止规则的问题，增强了研究和教育的基础设施。

Markov chain Monte Carlo (MCMC) has several disadvantages when compared to classical Monte Carlo methods. In particular, an important issue that every practitioner faces when implementing MCMC is when to stop the computation. Typically, a mixture of experience and ad hoc methods is employed to make this decision. Thus one is forced to wonder about the quality of the inference. The investigator studies sequential fixed-width methods that allow construction of an interval estimator for the quantity of interest. The interval estimator describes the confidence in the point estimate. The investigator uses this to study the development of valid stopping rules when the MCMC computation is aimed at estimating general quantities of the target distribution.These methods require the Markov chain to converge at a geometric rate which in turn implies there is a limiting distribution of the point estimate in the settings of interest. Thus the investigator studies the convergence rates of Markov chains encountered in two broad classes of Bayesian models.MCMC methods have become a standard technique in the toolbox of applied statisticians (and many scientists in other disciplines). Indeed, it is not much of an overstatement to say that it has revolutionized applied statistics, especially that of the Bayesian variety. Unfortunately, MCMC methods are not always used carefully leading to dubious claims in the literature. In particular, there has been little effort to include measures of uncertainty in inferential conclusions. Rigorously addressing the issue of stopping rules in terms of these measures of uncertainty enhances infrastructure for research and education by providing statisticians and other scientists valid techniques for using MCMC to make inference in their research setting.