Mixing Regimes for Adaptive Markov Chain Monte Carlo

计算复杂的积分是贝叶斯统计和科学中的中心计算问题。马尔可夫链蒙特卡罗（MCMC）是一种通用的计算工具，通过生成一系列保证收敛到所需积分的估计值来进行计算。MCMC的一大优点是它不需要太多的努力：即使是需要计算困难积分的新手用户也可以快速生成许多保证有效的MCMC算法。不幸的是，通常情况下，这些算法中的大多数效率太低而无法使用。因此，在实践中，用户必须花时间寻找“好的”MCMC算法。自适应MCMC（AMCMC）试图通过迭代地改进底层MCMC算法来自动化这个过程，因为它改进了积分的估计，最终学习到一个好的算法和一个好的积分估计。当成功时，AMCMC扩展了MCMC方法可以应用的问题的范围，而无需太多的用户努力。

Calculating complicated integrals is a central computational problem in Bayesian statistics and the sciences. Markov chain Monte Carlo (MCMC) is a general-purpose tool for doing this computation by generating a sequence of estimates that are guaranteed to converge to the desired integral. One of MCMC's great virtues is that it doesn't require too much effort: even novice users who need to calculate difficult integrals can quickly generate many MCMC algorithms that are guaranteed to work. Unfortunately, it is often the case that most of these algorithms are too inefficient to be useful. Thus, in practice users must spend time finding `good' MCMC algorithms. Adaptive MCMC (AMCMC) attempts to automate this process by iteratively refining the underlying MCMC algorithm as it improves its estimate of the integral, eventually learning both a good algorithm and a good estimate of the integral. When successful, AMCMC expands the range of problems for which MCMC methods can be applied without too much user effort.