Lin S, Thompson E, Wijsman E
Department of Statistics, University of California, Berkeley 94720.
Ann Hum Genet. 1994 Oct;58(4):343-57. doi: 10.1111/j.1469-1809.1994.tb00731.x.
Exact probability and likelihood computation on complex pedigrees is often infeasible, since exact methods are too computationally intensive even with today's computing technology. A statistical tool, Markov chain Monte Carlo (MCMC), is increasingly being explored as a technique for estimating probabilities of genotypic configurations on pedigrees conditional on phenotypic data. However, this conditional probability distribution on a complex pedigree is, in general, multimodal, and multimodality is one of the major difficulties in MCMC exploration of a probability surface. In this paper, a new member of the MCMC Metropolis-Hastings class of algorithms is proposed; the heated-Metropolis algorithm. The algorithm achieves passage through low probability states to other local modes of the probability distribution, and so provides much improved estimates of probabilities of interest. The example considered is the estimation of the probabilities of carrier genotype for the founders of a complex pedigree in which a very rare lethal recessive trait is segregating.
在复杂家系中进行精确概率和似然性计算通常是不可行的，因为即使使用当今的计算技术，精确方法的计算量也太大。一种统计工具，马尔可夫链蒙特卡罗（MCMC），正越来越多地被探索作为一种根据表型数据估计家系中基因型配置概率的技术。然而，复杂家系上的这种条件概率分布通常是多峰的，多峰性是MCMC探索概率曲面的主要困难之一。本文提出了MCMC Metropolis-Hastings算法类的一个新成员；热Metropolis算法。该算法实现了通过低概率状态到达概率分布的其他局部模式，从而提供了对感兴趣概率的显著改进估计。所考虑的例子是估计一个复杂家系创始人的携带者基因型概率，其中一种非常罕见的致死隐性性状正在分离。
