Modelling neuronal interactions using a directed network can be used to provide insight into the activity of the brain during experimental tasks. Magnetoencephalography (MEG) allows for the observation of the fast neuronal dynamics necessary to characterize the activity of sources and their interactions. A network representation of these sources and their connections can be formed by mapping them to nodes and their connection strengths to edge weights. Dynamic Causal Modelling (DCM) presents a Bayesian framework to estimate the parameters of these networks, as well as the ability to test hypotheses on the structure of the network itself using Bayesian model comparison. DCM uses a neurologically-informed representation of the active neural sources, which leads to an underdetermined system and increased complexity in estimating the network parameters. This work shows that inform- ing the MEG DCM source location with prior distributions defined using a MEG source localization algorithm improves model selection accuracy. DCM inversion of a group of candidate models shows an enhanced ability to identify a ground-truth network structure when source-localized prior means are used. / Master of Science

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Bioequivalence determines if two drugs are alike. The three kinds of bioequivalence are Average, Population, and Individual Bioequivalence. These Bioequivalence criteria can be evaluated using aggregate and disaggregate methods. Considerable work assessing bioequivalence in a frequentist method exists, but the advantages of Bayesian methods for Bioequivalence have been recently explored. Variance parameters are essential to any of theses existing Bayesian Bioequivalence metrics. Usually, the prior distributions for model parameters use either informative priors or vague priors. The Bioequivalence inference may be sensitive to the prior distribution on the variances. Recently, there have been questions about the routine use of inverse gamma priors for variance parameters. In this paper we examine the effect that changing the prior distribution of the variance parameters has on Bayesian models for assessing Bioequivalence and the carry-over effect. We explore our method with some real data sets from the FDA.

Statistical heterogeneity refers to differences among results of studies combined in a meta-analysis beyond that expected by chance. On the one hand, excessive heterogeneity can diminish power to discover genetic signals; on the other, moderate heterogeneity can reveal important biological differences among studies. Given its double-edged nature, this thesis dissects heterogeneity in genetic association meta-analyses from three vantage points. First, a novel multi-variant statistic, M is proposed to detect genome-wide (systematic) heterogeneity patterns in genetic association meta-analyses. This was motivated by the limited availability of appropriate methodology to measure the impact of heterogeneity across genetic signals, since traditional metrics (Q, I² and T²) measure heterogeneity at individual variants. Second, given that meta-analyses comprising small numbers of studies typically report imprecise summary effect estimates; GWAS-derived empirical heterogeneity priors are used to improve precision in estimation of average genetic effects and heterogeneity in smaller meta-analyses (e.g. ≤ 10 studies). Third, a critical evaluation of the Han-Eskin random-effects model shows how it can identify small effect heterogeneous loci overlooked by traditional fixed and random-effects methods. This work draws attention to the existence of genome-wide heterogeneity patterns, to reveal systematic differences among the ascertainment criteria of participating studies in a meta-analysis of coronary disease (CAD) risk. Furthermore, simulation studies with the Han-Eskin random-effects model revealed inflated genetic signals at small effect loci when heterogeneity levels were high. However, it did reveal an additional CAD risk variant overlooked by traditional meta-analysis methods. We therefore recommend a holistic approach to exploring heterogeneity in meta-analyses which assesses heterogeneity of genetic effects both at individual variants with traditional statistics and across multiple genetic signals with the M statistic. Furthermore, it is critically important to review forest plots for small effect loci identified using the Han-Eskin random-effects model amidst moderate-to-high heterogeneity (I² ≥ 40%).