ANNEALING MARKOV-CHAIN MONTE-CARLO WITH APPLICATIONS TO ANCESTRAL INFERENCE
ANNEALING MARKOV-CHAIN MONTE-CARLO WITH APPLICATIONS TO ANCESTRAL INFERENCE
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DOI：
10.1080/01621459.1995.10476590
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发表时间：
1995-09-01
影响因子：
3.7
通讯作者：
THOMPSON, EA
中科院分区：
文献类型：
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作者：
GEYER, CJ;THOMPSON, EA
马尔可夫链蒙特卡罗（MCMC；Metropolis-Hastings 算法）已用于许多统计问题，包括贝叶斯推理、似然推理和显着性检验。尽管该方法通常效果良好，但对收敛性的怀疑仍然存在。在这里，我们提出了与模拟退火密切相关的 MCMC 方法。我们的采样器混合速度足够快，足以解决其他方法需要大量计算时间的问题。它们模拟一系列分布的实现，允许模拟的分布随时间随机变化。如果分布序列选择得当，那么采样器将很好地混合并为所有分布生成准确的答案。即使只有一种感兴趣的分布，这些类似退火的采样器也可能是获得快速混合采样器的唯一已知方法。这些方法对于解决统计遗传学等领域出现的非常困难的问题至关重要。我们用一个应用程序来说明这些方法，该应用程序比 MCMC 以前解决的任何问题都困难得多，涉及对一个非常大的家谱（7 代，2,024 个人）的祖先推断。问题是根据活体个体的数据，找出每个个体成为囊性纤维化携带者的概率。精确计算这些条件概率是不可行的。此外，即使在可以想象的最快的计算机上，解决该问题的吉布斯采样器也无法在合理的时间内混合。我们的类退火采样器的混合时间为几个小时。我们还给出了“女巫帽”分布和条件施特劳斯过程的采样器示例。
Markov chain Monte Carlo (MCMC; the Metropolis-Hastings algorithm) has been used for many statistical problems, including Bayesian inference, likelihood inference, and tests of significance. Though the method generally works well, doubts about convergence often remain. Here we propose MCMC methods distantly related to simulated annealing. Our samplers mix rapidly enough to be usable for problems in which other methods would require eons of computing time. They simulate realizations from a sequence of distributions, allowing the distribution being simulated to vary randomly over time. If the sequence of distributions is well chosen, then the sampler will mix well and produce accurate answers for all the distributions. Even when there is only one distribution of interest, these annealing-like samplers may be the only known way to get a rapidly mixing sampler. These methods are essential for attacking very hard problems, which arise in areas such as statistical genetics. We illustrate the methods with an application that is much harder than any problem previously done by MCMC, involving ancestral inference on a very large genealogy (7 generations, 2,024 individuals). The problem is to find, conditional on data on living individuals, the probabilities of each individual having been a carrier of cystic fibrosis. Exact calculation of these conditional probabilities is infeasible. Moreover, a Gibbs sampler for the problem would not mix in a reasonable time, even on the fastest imaginable computers. Our annealing-like samplers have mixing times of a few hours. We also give examples of samplers for the ''witch's hat'' distribution and the conditional Strauss process.