Development of Evidential Methodology for Analysis of Genetic Data

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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.**