Perturbation bounds for Monte Carlo within Metropolis via restricted approximations
Perturbation bounds for Monte Carlo within Metropolis via restricted approximations
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DOI：
10.1016/j.spa.2019.06.015
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发表时间：
2018-09
影响因子：
1.4
通讯作者：
F. Medina-Aguayo;Daniel Rudolf;Nikolaus Schweizer
中科院分区：
文献类型：
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作者：
F. Medina-Aguayo;Daniel Rudolf;Nikolaus Schweizer
蒙特卡洛大都会内（MCwM）算法是一种扰动大都会-黑斯廷斯（MH）算法，它提供了一种在目标分布难以处理时进行近似采样的方法。假设无扰动马尔可夫链是几何遍历的，我们给出了摄动MCwM和无扰动MH链的n阶分布之差的显式估计。这些边界是基于马尔科夫链的新的摄动结果，这些结果超出了MCwM的设定。为了应用该边界，我们需要控制两条链的转移概率之差，并验证扰动链的稳定性。
Abstract The Monte Carlo within Metropolis (MCwM) algorithm, interpreted as a perturbed Metropolis–Hastings (MH) algorithm, provides an approach for approximate sampling when the target distribution is intractable. Assuming the unperturbed Markov chain is geometrically ergodic, we show explicit estimates of the difference between the n th step distributions of the perturbed MCwM and the unperturbed MH chains. These bounds are based on novel perturbation results for Markov chains which are of interest beyond the MCwM setting. To apply the bounds, we need to control the difference between the transition probabilities of the two chains and to verify stability of the perturbed chain.