Globally Centered Autocovariances in MCMC
提出一种全局中心的自协方差函数估计量，相比现有方法偏差更小，在自相关图、渐近协方差矩阵和有效样本量估计三个输出分析应用中表现更优。
Autocovariances are a fundamental quantity of interest in Markov chain Monte Carlo (MCMC) simulations with autocorrelation function (ACF) plots being an integral visualization tool for performance assessment. Unfortunately, for slow-mixing Markov chains, the empirical autocovariance can highly underestimate the truth. For multiple-chain MCMC sampling, we propose a globally centered estimator of the autocovariance function (G-ACvF) that exhibits significant theoretical and empirical improvements. We show that the bias of the G-ACvF estimator is smaller than the bias of the current state-of-the-art. The impact of this improved estimator is evident in three critical output analysis applications: (a) ACF plots, (b) estimates of the Monte Carlo asymptotic covariance matrix, and (c) estimates of the effective sample size. Under weak conditions, we establish strong consistency of our improved asymptotic covariance estimator, and obtain its large-sample bias and variance. The performance of the new estimators is demonstrated through various examples. Supplementary materials for this article are available online.