Notes on the maximum likelihood estimation of haplotype frequencies
Notes on the maximum likelihood estimation of haplotype frequencies
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DOI：
10.1046/j.1529-8817.2003.00088.x
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发表时间：
2004-05-01
影响因子：
1.9
通讯作者：
Gojobori, T
中科院分区：
文献类型：
--
作者：
Mano, S;Yasuda, N;Gojobori, T
最大似然估计（MLE）是估计连锁相位未知的基因型群体单倍型频率最常用的方法之一。MLE通常使用期望最大化（EM）算法来实现。已知EM算法具有估计器可能错误地收敛到似然曲面的局部最大值或鞍点之一的风险，从而导致单倍型频率的MLE中的严重错误。本文通过理论处理，给出了似然曲面上出现局部极大值或鞍点的充要条件。作为经验法则，相位已知个体中的耦合和排斥单体型频率之间的差异是相位模糊个体的频率的3/2倍，这是似然曲面是单峰的充分条件。此外，我们给出了双等位基因两位点问题的解析解，并构造了一个通用的算法来获得全局最大值。
The maximum likelihood estimation (MLE) is one of the most popular ways to estimate haplotype frequencies of a population with genotype data whose linkage phases are unknown. The MLE is commonly implemented in the use of the Expectation-Maximization (EM) algorithm. It is known that the EM algorithm carries the risk that an estimator may converge erroneously to one of the local maxima or saddle points of the likelihood surface, resulting in serious errors in the MLE of haplotype frequencies. In this note, by theoretical treatments we present the necessary and sufficient conditions that the local maxima or saddle points on the likelihood surface appear. As a rule of thumb, that the difference between the coupling and repulsive haplotype frequencies in phase known individuals is 3/2 times larger than the frequency of phase ambiguous individuals is the sufficient condition that the likelihood surface is unimodal. Moreover, we present the analytic solution to the biallelic two-locus problem, and construct a general algorithm to obtain the global maximum.