Lin S, Thompson E, Wijsman E
Department of Statistics, University of California, Berkeley 94720.
Am J Hum Genet. 1994 Apr;54(4):695-704.
Markov chain Monte Carlo (MCMC) has recently gained use as a method of estimating required probability and likelihood functions in pedigree analysis, when exact computation is impractical. However, when a multiallelic locus is involved, irreducibility of the constructed Markov chain, an essential requirement of the MCMC method, may fail. Solutions proposed by several researchers, which do not identify all the noncommunicating sets of genotypic configurations, are inefficient with highly polymorphic loci. This is a particularly serious problem in linkage analysis, because highly polymorphic markers are much more informative and thus are preferred. In the present paper, we describe an algorithm that finds all the noncommunicating classes of genotypic configurations on any pedigree. This leads to a more efficient method of defining an irreducible Markov chain. Examples, including a pedigree from a genetic study of familial Alzheimer disease, are used to illustrate how the algorithm works and how penetrances are modified for specific individuals to ensure irreducibility.
马尔可夫链蒙特卡罗（MCMC）方法最近开始被用作一种在系谱分析中估计所需概率和似然函数的方法，当精确计算不切实际时。然而，当涉及多等位基因位点时，所构建的马尔可夫链的不可约性（这是MCMC方法的一个基本要求）可能会失效。几位研究人员提出的解决方案，未能识别出所有非连通的基因型配置集，对于高度多态性位点来说效率低下。这在连锁分析中是一个特别严重的问题，因为高度多态性标记的信息量大得多，因此更受青睐。在本文中，我们描述了一种算法，该算法可以找到任何系谱上所有非连通的基因型配置类。这导致了一种定义不可约马尔可夫链的更有效方法。文中给出了一些例子，包括来自家族性阿尔茨海默病遗传研究的一个系谱，来说明该算法的工作原理以及如何针对特定个体修改外显率以确保不可约性。
