MCMC中的全局中心自协方差
Globally-centered autocovariances in MCMC
摘要：
自协方差是马尔可夫链蒙特卡罗（MCMC）模拟中的一个基本量，自相关函数（ACF）图是性能评估的整体可视化工具。不幸的是，对于慢混合马尔可夫链，经验自协方差可能会大大低估真相。对于多链MCMC抽样，我们提出了一个全局中心估计的自协方差函数（G-ACvF），表现出显着的理论和经验改进。我们表明，G-ACvF估计的偏差小于当前最先进的偏差。这种改进的估计的影响是显而易见的，在三个关键的输出分析应用：（1）ACF图，（2）估计的蒙特卡罗渐近协方差阵，（3）估计的有效样本量。在较弱的条件下，我们建立了改进的渐近协方差估计的强相合性，并得到了它的大样本偏差和方差。新的估计的性能通过各种例子证明。
英文摘要：
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: (1) ACF plots, (2) estimates of the Monte Carlo asymptotic covariance matrix, and (3) 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.
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