标题： 详细平衡原理与马尔可夫链蒙特卡罗方法和模拟退火的收敛性评估 显示英文标题

标题： Principle of detailed balance and convergence assessment of Markov Chain Monte Carlo methods and simulated annealing

摘要： 马尔可夫链蒙特卡罗（MCMC）方法用于从给定的目标分布中进行抽样，当该分布不存在于闭合形式中，或者即使存在闭合形式，也没有有效的方法从中独立抽样时。 尽管在过去二十年中已经提出了大量用于评估MCMC方法收敛性的诊断工具，但寻找一种可靠且易于实现的工具仍在继续。 本文提出了一种基于细致平衡原理的标准，该标准提供了对给定链收敛性的定性评估。 该标准基于一个一维统计量的行为，在平稳性的假设下推导了其渐近分布；我们的结果在弱条件下适用，并具有完全直观的优势。 我们将这一标准作为模拟退火中的停止规则，用于求解20组分混合模型参数的最大似然估计器的问题。 我们还将它应用于通过切片抽样和梅特ropolis-哈斯廷斯算法从10维漏斗分布中抽样的问题。 此外，基于此收敛准则，我们定义了一个算法相对于另一个算法的效率度量。 显示英文摘要

摘要： Markov Chain Monte Carlo (MCMC) methods are employed to sample from a given distribution of interest, whenever either the distribution does not exist in closed form, or, if it does, no efficient method to simulate an independent sample from it is available. Although a wealth of diagnostic tools for convergence assessment of MCMC methods have been proposed in the last two decades, the search for a dependable and easy to implement tool is ongoing. We present in this article a criterion based on the principle of detailed balance which provides a qualitative assessment of the convergence of a given chain. The criterion is based on the behaviour of a one-dimensional statistic, whose asymptotic distribution under the assumption of stationarity is derived; our results apply under weak conditions and have the advantage of being completely intuitive. We implement this criterion as a stopping rule for simulated annealing in the problem of finding maximum likelihood estimators for parameters of a 20-component mixture model. We also apply it to the problem of sampling from a 10-dimensional funnel distribution via slice sampling and the Metropolis-Hastings algorithm. Furthermore, based on this convergence criterion we define a measure of efficiency of one algorithm versus another.