Baur M P, Elston R C, Gürtler H, Henningsen K, Hummel K, Matsumoto H, Mayr W, Moris J W, Niejenhuis L, Polesky H
Am J Hum Genet. 1986 Oct;39(4):528-36.
In a recent publication, Li and Chakravarti claim to have shown that the paternity index is not a likelihood ratio. They present a method of estimating the prior probability of paternity from a sample of previous court cases on the basis of exclusions and nonexclusions. They propose calculating the posterior probability on the basis of this estimated prior and the test result expressed as exclusion/nonexclusion. Their claim is wrong--the paternity index is a likelihood-ratio, that is, the ratio of the likelihood of the observation conditional on the two mutually exclusive hypotheses. Their proposed method of estimating the prior has been long known, has been applied to several samples, and is inferior (in terms of variance of the estimate) to maximum likelihood estimation based on all the phenotypic information available. Their proposed "new method" of calculating a posterior probability is based on the use of a less informative likelihood ratio 1/(1-PE) instead of Gürtler's fully informative paternity index X/Y (Acta Med Leg Soc Liege 9:83-93, 1956), but is otherwise identical to the Bayesian approach originally introduced by Essen-Möller in 1938.
在最近的一篇出版物中，李和查克拉瓦蒂声称已经证明父权指数不是一个似然比。他们提出了一种基于先前法庭案例样本，根据排除和未排除情况来估计父权先验概率的方法。他们提议基于这个估计的先验概率以及表示为排除/未排除的检测结果来计算后验概率。他们的说法是错误的——父权指数是一个似然比，也就是说，是在两个相互排斥的假设条件下观察到的似然性的比率。他们提议的估计先验概率的方法早已为人所知，已经应用于多个样本，并且（就估计的方差而言）不如基于所有可用表型信息的最大似然估计。他们提议的计算后验概率的“新方法”是基于使用信息量较少的似然比1/(1 - PE)，而不是居特勒的信息完全的父权指数X/Y（《列日医学法律学会学报》9:83 - 93，1956年），但在其他方面与埃森 - 默勒于1938年最初引入的贝叶斯方法相同。
