论文标题
MCMC中以全球为中心的自动助力
Globally-centered autocovariances in MCMC
论文作者
论文摘要
自动载体是马尔可夫链蒙特卡洛（MCMC）模拟具有自相关功能（ACF）图的基本兴趣，是用于性能评估的整体可视化工具。不幸的是，对于慢速混合马尔可夫连锁店，经验的自动加以高度低估了事实。对于多链MCMC采样，我们提出了一个以全球为中心的自动助力函数（G-ACVF）的估计值，该估计值具有显着的理论和经验改进。我们表明，G-ACVF估计量的偏差小于当前最新面临的偏差。在三个关键输出分析应用中，这一改进的估计器的影响很明显：（1）ACF图，（2）蒙特卡洛渐近协方差矩阵的估计值，以及（3）有效样本量的估计值。在弱条件下，我们建立了改进的渐近协方差估计器的强大一致性，并获得其大样本偏差和方差。通过各种示例证明了新估计器的性能。
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.
