R*: A Robust MCMC Convergence Diagnostic with Uncertainty Using Decision Tree Classifiers
R*: A Robust MCMC Convergence Diagnostic with Uncertainty Using Decision Tree Classifiers
复制标题
DOI：
10.1214/20-ba1252
复制
发表时间：
2022-06-01
影响因子：
4.4
通讯作者：
Vehtari, Aki
中科院分区：
文献类型：
--
作者：
Lambert, Ben;Vehtari, Aki
在过去的三十年里，马尔可夫链蒙特卡罗（MCMC）已经改变了贝叶斯模型的推理：主要是因为这个，贝叶斯推理现在是应用科学家的主力。在一般情况下，MCMC采样渐近收敛于后验分布，但这并不能保证其在有限时间内的性能。监测收敛性的主要方法是运行多个链并监测单个链的特征，并将其与总体进行比较：如果链内和链间的汇总具有可比性，则这表明链已收敛到共同的平稳分布。在这里，我们介绍了一种基于机器学习分类器模型如何成功区分单个链来诊断收敛的新方法。我们将此收敛度量称为R*。与占主导地位的（R）超过上限相比，R* 是所有参数的单一统计量，表明缺乏混合，尽管也可以确定单个变量对该度量的重要性。此外，R* 不是基于抽样分布的任何单一特征;相反，它使用链中的所有信息，包括联合抽样分布所提供的信息，而这一点目前在很大程度上被现有方法所忽视。我们建议使用两种不同的机器学习分类器来计算R*-梯度提升回归树和随机森林-它们在不同维度的模型中都能很好地工作。由于这些方法中的每一种都输出分类概率，因此作为副产品，我们获得了R* 的不确定性。该方法是简单的实施，并可能是一个补充的额外检查MCMC收敛应用分析。
Markov chain Monte Carlo (MCMC) has transformed Bayesian model inference over the past three decades: mainly because of this, Bayesian inference is now a workhorse of applied scientists. Under general conditions, MCMC sampling converges asymptotically to the posterior distribution, but this provides no guarantees about its performance in finite time. The predominant method for monitoring convergence is to run multiple chains and monitor individual chains' characteristics and compare these to the population as a whole: if within-chain and between-chain summaries are comparable, then this is taken to indicate that the chains have converged to a common stationary distribution. Here, we introduce a new method for diagnosing convergence based on how well a machine learning classifier model can successfully discriminate the individual chains. We call this convergence measure R*. In contrast to the predominant (R) over cap, R* is a single statistic across all parameters that indicates lack of mixing, although individual variables' importance for this metric can also be determined. Additionally, R* is not based on any single characteristic of the sampling distribution; instead it uses all the information in the chain, including that given by the joint sampling distribution, which is currently largely overlooked by existing approaches. We recommend calculating R* using two different machine learning classifiers - gradient-boosted regression trees and random forests - which each work well in models of different dimensions. Because each of these methods outputs a classification probability, as a byproduct, we obtain uncertainty in R*. The method is straightforward to implement and could be a complementary additional check on MCMC convergence for applied analyses.