论文标题
从可逆的马尔可夫链中对自动增强序列的有效形状约束推断
Efficient shape-constrained inference for the autocovariance sequence from a reversible Markov chain
论文作者
论文摘要
在本文中，我们研究了估计由可逆的马尔可夫链引起的自相关序列的问题。研究此问题的激励应用是对马尔可夫链中心极限定理中渐近方差的估计。我们提出了一个新型的形状受限估计量，对自动增强序列序列的估计值是基于关键观察结果，即自动练习序列作为矩序列的表示性施加了某些形状约束。我们检查了提出的估计器的理论特性，并为我们的估计器提供了强大的一致性保证。特别是，对于几何可逆的马尔可夫链，我们表明，相对于$ \ ell_2 $距离的真实自动练习序列非常一致，并且我们的估计器会导致对渐近方差的强烈一致的估计。最后，我们进行了经验研究来说明所提出的估计量的理论特性，并证明了与其他当前的马尔可夫链Carlo方差估计的当前最新方法相比，我们的估计量的有效性，包括批次平均值，光谱方差估计器和初始凸序估计器。
In this paper, we study the problem of estimating the autocovariance sequence resulting from a reversible Markov chain. A motivating application for studying this problem is the estimation of the asymptotic variance in central limit theorems for Markov chains. We propose a novel shape-constrained estimator of the autocovariance sequence, which is based on the key observation that the representability of the autocovariance sequence as a moment sequence imposes certain shape constraints. We examine the theoretical properties of the proposed estimator and provide strong consistency guarantees for our estimator. In particular, for geometrically ergodic reversible Markov chains, we show that our estimator is strongly consistent for the true autocovariance sequence with respect to an $\ell_2$ distance, and that our estimator leads to strongly consistent estimates of the asymptotic variance. Finally, we perform empirical studies to illustrate the theoretical properties of the proposed estimator as well as to demonstrate the effectiveness of our estimator in comparison with other current state-of-the-art methods for Markov chain Monte Carlo variance estimation, including batch means, spectral variance estimators, and the initial convex sequence estimator.
