Estimating Convergence of Markov chains with L-Lag Couplings
Estimating Convergence of Markov chains with L-Lag Couplings
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发表时间：
2019-05
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通讯作者：
N. Biswas;P. Jacob;Paul Vanetti
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作者：
N. Biswas;P. Jacob;Paul Vanetti
马尔可夫链蒙特卡罗（MCMC）方法生成的样本是渐近分布的目标分布的利益，随着迭代次数达到无穷大。各种理论结果提供了一个固定数量的迭代后的目标和边缘分布之间的距离上界。这些上限是在个案的基础上，通常涉及棘手的数量，这限制了他们的使用从业者。我们引入L-滞后耦合产生可计算的，非渐近的上限估计的总变差或Wasserstein距离一般马尔可夫链。我们应用L-lag耦合的任务（i）确定MCMC老化，（ii）比较不同的MCMC算法与相同的目标，（iii）比较准确和近似的MCMC。最后，我们（iv）评估顺序蒙特卡罗和自归一化重要性采样器的偏差。
Markov chain Monte Carlo (MCMC) methods generate samples that are asymptotically distributed from a target distribution of interest as the number of iterations goes to infinity. Various theoretical results provide upper bounds on the distance between the target and marginal distribution after a fixed number of iterations. These upper bounds are on a case by case basis and typically involve intractable quantities, which limits their use for practitioners. We introduce L-lag couplings to generate computable, non-asymptotic upper bound estimates for the total variation or the Wasserstein distance of general Markov chains. We apply L-lag couplings to the tasks of (i) determining MCMC burn-in, (ii) comparing different MCMC algorithms with the same target, and (iii) comparing exact and approximate MCMC. Lastly, we (iv) assess the bias of sequential Monte Carlo and self-normalized importance samplers.