Development of Evidential Methodology for Analysis of Genetic Data

遗传学领域需要新的统计方法来处理日益增长的数据集和复杂性。统计范式，惩罚调查人员彻底询问他们的数据(即。多重假设检验问题)将失宠。证据范式(EP)是频率范式和贝叶斯范式的另一种鲜为人知的替代方法，它使用两个简单假设的似然比(LR)来衡量给定数据体中的相对证据强度。通过LRS解释证据强度是可靠的，其中假设的假值很少比真值得到更好的支持，并且观察到有利于假值的证据的概率M可以由样本大小控制。但M不影响对给定数据体中证据强度的解释，该数据体由LR表示。由于错误概率和证据强度的这种脱钩，我们已经证明，由于评估多个假设，确实存在M的增加，但这可以通过重复研究来控制，这是遗传学领域的常规做法。*我们开发了用于分析遗传数据的EP统计方法。作为一个新的领域，无论是在方法开发方面，还是在培养下一代EP研究人员方面，都有很多工作要做。我们以前的贡献为其他研究提供了新的研究方向，包括我们在遗传连锁和病例对照关联研究的EP方法学方面的工作，以及多种假设检验方法。我们和其他人最近的理论发展填补了重要的理论空白：对可能性的稳健调整可以使EP对模型错误指定具有稳健性；而可能性定律的推广为复合假设提供了一个权衡证据的框架。在这里，我们提出了三个具体的项目：(1)使复合似然方法对相关数据的EP遗传关联分析具有健壮性；(2)推导出广义似然定律的操作特征；(3)开发健壮的EP关联方法，以整合来自不同技术的大型基因组数据集。*EP提供了一种直观的、与遗传学家产生共鸣的基因组数据分析方法，并为阻碍进展的问题提供了独特的解决方案。然而，缺乏EP方法来解决统计遗传学中的及时问题限制了它的应用。在这里，我们提出了一个研究计划，重点是为最先进的基因组应用开发EP方法，这有助于朝着衡量统计证据的合理理论发展。**

The genetics field is in need of novel statistical methodology to deal with data sets of growing size and complexity. Statistical paradigms that penalize investigators for thoroughly interrogating their data (ie. the multiple hypothesis testing problem) will fall out of favour. The evidential paradigm (EP), a less-known alternative to Frequentist and Bayesian paradigms, uses the likelihood ratio (LR) for two simple hypotheses to measure the relative evidence strength in a given body of data. Interpreting evidence strength via LRs is reliable, where false values for the hypotheses are rarely better supported than true values, and the probability of observing evidence favouring false values, M, can be controlled by the sample size. But M does not affect the interpretation of the evidence strength in a given body of data, which is represented by the LR. Due to this decoupling of error probabilities and evidence strength we have shown that, indeed, there is an increase in M due to assessing multiple hypotheses, but this can be controlled by a replication study; a routine practice in the genetics field.***We develop EP statistical methodology for the analysis of genetic data. As a new field there is much work to be done, both in methods development and in training the next generation of EP researchers. Our previous contributions have spurred new research directions for others, including our work in EP methodology for genetic linkage and case-control association studies, and multiple hypothesis testing approaches. Recent theoretical developments by us and others have served to fill important theoretical gaps: Robust adjustments to likelihoods can make the EP robust to model misspecification; while generalizations of the Law of Likelihood provide a framework to weigh evidence for composite hypotheses. Here we propose three specific projects: (1) making composite likelihoods robust for EP genetic association analysis of correlated data; (2) derive the operational characteristics of the generalized Law of Likelihood; and (3) develop robust EP association methodology to integrate large genomic data sets from different technologies.***The EP provides an approach to the analysis of genomic data that is intuitive, resonates with geneticists, and provides unique solutions to issues that hamper progress. However, an absence of EP methodology to address timely problems in statistical genetics limits its application. Here we present a program of research focused on developing EP methodology for state-of-the-art genomic applications, that contribute to theoretical developments towards a sound theory for measuring statistical evidence.**