标题： 不可识别的家系和一种贝叶斯解决方案 显示英文标题

标题： Non-Identifiable Pedigrees and a Bayesian Solution

摘要： 一些方法旨在校正或检验关系或重建家谱，或家族树。 我们表明，由于家谱似然的可识别性，即在家谱模型下继承数据的概率，这些方法无法解决正确关系的歧义。 这意味着没有任何基于似然的方法可以以高概率产生正确的家谱推断。 这种不可靠性对于健康和法医学应用都至关重要。 在本文中，我们首次讨论了非同构家谱中的多个类型个体，$\mathcal{P}$和$\mathcal{Q}$，其中似然是不可识别的，$Pr[G~|~\mathcal{P},\theta] = Pr[G~|~\mathcal{Q},\theta]$，对于所有输入数据$G$和所有重组率参数$\theta$。 虽然之前已知不可识别对，但我们给出一个具有多个个体数据的例子。 此外，还提供了对驱动这些不可识别性例子的通用离散结构的更深入理解，以及指导算法仅检查可识别家谱的结果。 本文引入了一个通用标准，用于确定一对家谱是否不可识别，以及两个易于计算的标准，保证可识别性。 最后，我们建议一种处理不可识别似然的方法：使用贝叶斯规则从似然和先验中获得后验。 我们提出了一种先验，保证后验能够区分所有家谱对。 缩短版发表为：B. Kirkpatrick。 不可识别的家谱和贝叶斯解决方案。 国际生物信息学研究与应用研讨会（ISBRA），7292:139-152 2012。 显示英文摘要

摘要： Some methods aim to correct or test for relationships or to reconstruct the pedigree, or family tree. We show that these methods cannot resolve ties for correct relationships due to identifiability of the pedigree likelihood which is the probability of inheriting the data under the pedigree model. This means that no likelihood-based method can produce a correct pedigree inference with high probability. This lack of reliability is critical both for health and forensics applications. In this paper we present the first discussion of multiple typed individuals in non-isomorphic pedigrees, $\mathcal{P}$ and $\mathcal{Q}$, where the likelihoods are non-identifiable, $Pr[G~|~\mathcal{P},\theta] = Pr[G~|~\mathcal{Q},\theta]$, for all input data $G$ and all recombination rate parameters $\theta$. While there were previously known non-identifiable pairs, we give an example having data for multiple individuals. Additionally, deeper understanding of the general discrete structures driving these non-identifiability examples has been provided, as well as results to guide algorithms that wish to examine only identifiable pedigrees. This paper introduces a general criteria for establishing whether a pair of pedigrees is non-identifiable and two easy-to-compute criteria guaranteeing identifiability. Finally, we suggest a method for dealing with non-identifiable likelihoods: use Bayes rule to obtain the posterior from the likelihood and prior. We propose a prior guaranteeing that the posterior distinguishes all pairs of pedigrees. Shortened version published as: B. Kirkpatrick. Non-identifiable pedigrees and a Bayesian solution. Int. Symp. on Bioinformatics Res. and Appl. (ISBRA), 7292:139-152 2012.