STA 290 Seminar Series
Tuesday, May 10th, 4:10pm, MSB 1147 (Colloquium Room)
Refreshments at 3:30pm in MSB 4110 (Statistics Lounge)
Speaker: Tingting Zhang (Department of Statistics, University of Virginia)
Title: “Bayesian Inference of High-Dimensional, Cluster-Structured Ordinary Differential Equation Models with Applications to Brain Connectivity Studies”
Abstract: We use ordinary differential equations (ODEs) to model the human brain as a continuous-time dynamic system whose components, i.e., brain regions, biophysically interact with each other. In contrast to existing ODE models that focus on directional connectivity among only a few brain regions and that rely on strong prior belief of the existence and strength of connections, we propose a high-dimensional ODE model motivated by statistical considerations to explore connectivity among multiple small brain regions. The new model, called the modular and indicator-based dynamic directional model (MIDDM), features a cluster structure consisting of modules of densely connected brain regions, and uses indicators to denote significant directional interactions among brain regions. We develop a unified Bayesian framework for quantifying uncertainty in the assumed ODE model, identifying clusters, selecting strongly connected brain regions, and making inferences about the MIDDM. The prior distributions in the Bayesian model for MIDDM parameters are carefully designed such that the ensuing joint posterior distributions for ODE state functions and the MIDDM parameters have well-defined and easy-to-simulate posterior conditional distributions. To further speed up the posterior simulation, we employ parallel computing schemes in two Markov Chain Monte Carlo steps. We show that the proposed Bayesian approach outperforms an optimization-based method for ODE estimation through both simulation studies and analysis of an auditory electrocorticography dataset.