不可识别谱系和贝叶斯解
Non-Identifiable Pedigrees and a Bayesian Solution
摘要：
一些方法旨在纠正或测试关系或重建谱系或家谱。我们表明，这些方法不能解决关系，由于系谱可能性，这是继承数据的系谱模型下的概率的可识别性正确的关系。这意味着没有基于似然性的方法可以产生具有高概率的正确谱系推断。这种可靠性的缺乏对于健康和取证应用都是至关重要的。在本文中，我们提出了第一次讨论的多个类型的个人在非同构谱系，$\mathcal{P}$和$\mathcal{Q}$，其中的可能性是不可识别的，$Pr[G~|~\mathcal{P},θ] = Pr[G~|~\mathcal{Q},θ]$，所有输入数据$G$和所有重组率参数$θ$。虽然以前有已知的不可识别的对，我们给出了一个例子，有多个人的数据。此外，已经提供了对驱动这些不可识别性示例的一般离散结构的更深入理解，以及指导希望仅检查可识别谱系的算法的结果。本文介绍了一个确定一对家系是否不可识别的一般标准和两个易于计算的保证可识别性的标准。最后，我们提出了一种处理不可识别似然的方法：利用贝叶斯规则从似然和先验中获得后验。我们提出了一个事先保证后区分所有对谱系。简化版本发布为：B。柯克帕特里克不可识别的谱系和贝叶斯解决方案。国际Symp.和应用（ISBRA），7292：139-152 2012。
英文摘要：
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, $Pr[G~|~\mathcal{P},θ] = Pr[G~|~\mathcal{Q},θ]$, for all input data $G$ and all recombination rate parameters $θ$. 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
