Advancing Effective Connectivity Analysis: Robust and Sparse Group Dynamic Causal Modeling via Extended Parametric Empirical Bayes

Dynamic Causal Modeling (DCM) provides a principled framework for estimating effective connectivity in neuroimaging data, with Parametric Empirical Bayes (PEB) enabling hierarchical inference across sessions and subjects. However, standard PEB assumes Gaussian distributions at all hierarchical levels and employs conventional shrinkage priors that do not enforce true sparsity, limiting robustness to outlying subjects and reducing sensitivity to parsimonious connectivity structures. This thesis introduces a robust, sparsity-inducing hierarchical extension to DCM-PEB that addresses these limitations through two key innovations. First, a Student-t group-level likelihood replaces the conventional Gaussian likelihood, automatically downweighting outlying subject-level parameters using adaptive precision weights while retaining computational tractability via a normal-gamma scale mixture representation. Second, spike-and-slab priors with sparsity-inducing nonlocal moment (MOM) slab components replace conventional Gaussian priors, enforcing stronger separation between null and non-null effects by assigning zero density at the null value and penalizing small, spurious nonzero effects. Posterior inference is performed using an expectation-maximization (EM) algorithm that alternates between computing Student-t weights in the E-step and updating group-level parameters via coordinate-wise Newton optimization in the M-step. The proposed framework is applied to the openly shared NARPS dataset to examine effective connectivity underlying risky decision-making and loss aversion in gain-dominant versus loss-dominant gambles. Overall, this methodology provides a principled, robust, and interpretable approach to hierarchical effective connectivity analysis in heterogeneous populations and high-dimensional parameter spaces.