标题： 退火重要性采样 显示英文标题

标题： Annealed Importance Sampling

摘要： 模拟退火——通过一系列中间分布从易处理的分布转移到感兴趣的分布——传统上被用作一种处理马尔可夫链采样器中孤立模式的非精确方法。 在这里，展示了如何利用这种退火序列的马尔可夫链转移来定义一个重要性采样器。 马尔可夫链方面使得该方法即使在高维问题中也能表现良好，因为在这些情况下找到好的重要性采样分布会非常困难，而使用重要性权重可以确保随着退火运行次数的增加，所得到的估计值会收敛到正确值。 这种退火重要性采样过程类似于之前研究过的温度转换的后半部分，并可以被视为一种最近提出的顺序重要性采样的变体的推广。 它还与用于估计归一化常数比值的热力学积分方法有关。 当存在孤立模式或需要归一化常数的估计时，退火重要性采样最为吸引人，但它可能更普遍有用，因为其独立采样允许绕过评估马尔可夫链采样器中的收敛性和自相关性的某些问题。 显示英文摘要

摘要： Simulated annealing - moving from a tractable distribution to a distribution of interest via a sequence of intermediate distributions - has traditionally been used as an inexact method of handling isolated modes in Markov chain samplers. Here, it is shown how one can use the Markov chain transitions for such an annealing sequence to define an importance sampler. The Markov chain aspect allows this method to perform acceptably even for high-dimensional problems, where finding good importance sampling distributions would otherwise be very difficult, while the use of importance weights ensures that the estimates found converge to the correct values as the number of annealing runs increases. This annealed importance sampling procedure resembles the second half of the previously-studied tempered transitions, and can be seen as a generalization of a recently-proposed variant of sequential importance sampling. It is also related to thermodynamic integration methods for estimating ratios of normalizing constants. Annealed importance sampling is most attractive when isolated modes are present, or when estimates of normalizing constants are required, but it may also be more generally useful, since its independent sampling allows one to bypass some of the problems of assessing convergence and autocorrelation in Markov chain samplers.