Markov chain Monte Carlo convergence assessment via two-way analysis of variance
Markov chain Monte Carlo convergence assessment via two-way analysis of variance
复制标题
DOI：
10.2307/1390654
复制
发表时间：
2000-06-01
影响因子：
2.4
通讯作者：
Giudici, P
中科院分区：
文献类型：
--
作者：
Brooks, SP;Giudici, P
在这篇文章中，我们讨论的问题，评估马尔可夫链蒙特卡罗（MCMC）算法的模拟输出的基础上的性能。从本质上讲，我们扩展了Gelman和Rubin以及最近的布鲁克斯和Gelman的原始思想，使我们能够将MCMC模拟输出中固有的变化分为两个不同的组。我们展示了如何这样的诊断可能是有用的MCMC采样器解决模型选择问题，如可逆跳MCMC算法的性能评估。在模型选择的背景下，我们展示了如何使用可逆跳跃MCMC模拟输出来评估收敛性，这些参数在整个模拟过程中保持一致的解释：通过考虑该参数的采样方差的各种分解，我们可以根据模型内部和模型之间的混合特性来评估MCMC采样器的性能，并在图形中说明我们的方法高斯模型和正态混合背景。最后，我们提供了一个例子，我们的诊断评估不同的初始值对MCMC模拟输出的影响，从而说明了我们的方法超越贝叶斯模型选择和可逆跳MCMC上下文的更广泛的实用性。
In this article we discuss the problem of assessing the performance of Markov chain Monte Carlo (MCMC) algorithms on the basis of simulation output. In essence, we extend the original ideas of Gelman and Rubin and, more recently, Brooks and Gelman, to problems where we are able to split the variation inherent within the MCMC simulation output into two distinct groups. We show how such a diagnostic may be useful in assessing the performance of MCMC samplers addressing model choice problems, such as the reversible jump MCMC algorithm. In the model choice context, we show how the reversible jump MCMC simulation output for parameters that retain a coherent interpretation throughout the simulation, can be used to assess convergence: By considering various decompositions of the sampling variance of this parameter, we can assess the performance of our MCMC sampler in terms of its mixing properties both within and between models and we illustrate our approach in both the graphical Gaussian models and normal mixtures context. Finally, we provide an example of the application of our diagnostic to the assessment of the influence of different starting values on MCMC simulation output, thereby illustrating the wider utility of our method beyond the Bayesian model choice and reversible jump MCMC context.