再生MCMC算法估计误差的非渐近界
Nonasymptotic bounds on the estimation error for regenerative MCMC algorithms
摘要：
MCMC方法用于贝叶斯统计中，不仅用于从后验分布中采样，而且用于估计期望值。底层函数通常定义在连续状态空间上，并且可以是无界的。我们考虑再生设置和蒙特卡罗估计的基础上i.i.d.马尔可夫链轨迹的块。主要结果是均方误差的不等式。我们还考虑了置信区间。我们首先得到的结果的渐近方差，然后绑定的渐近方差一致遍历和几何遍历马尔可夫链。
英文摘要：
MCMC methods are used in Bayesian statistics not only to sample from posterior distributions but also to estimate expectations. Underlying functions are most often defined on a continuous state space and can be unbounded. We consider a regenerative setting and Monte Carlo estimators based on i.i.d. blocks of a Markov chain trajectory. The main result is an inequality for the mean square error. We also consider confidence bounds. We first derive the results in terms of the asymptotic variance and then bound the asymptotic variance for both uniformly ergodic and geometrically ergodic Markov chains.
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