Bayesian Inference for High-Dimensional Dynamic Systems Modeled by Ordinary Differential Equations with Applications to Brain Networks

• Activity Number: 123
• Type: Topic Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Tingting Zhang* and Brian Caffo and Dana Boatman and Qiannan Yin
• Companies: University of Virginia and The Johns Hopkins University and The Johns Hopkins University and University of Virginia
• Keywords: Bayesian Inference ; Ordinary Differential Equations ; Brain networks ; Modularity ; High dimensionality

Abstract

We use ordinary differential equations (ODEs) to model the human brain as a continuous-time physical system with directional interactions between its components, i.e., brain regions. Since modularity, where a large network is decomposable into several functionally independent small subnetworks/modules, has been widely reported in the scientific literature on brain networks, we proposed a new ODE model, called the Potts and indicator-based dynamic directional model (PIDDM), for brain directional networks, which features modularity and distinguishes significant directional interactions among brain regions from void ones. To perform the inference for PIDDM and also to provide a new statistical framework, in which high-dimensional ODE models can be estimated quickly, we construct a Bayesian hierarchical model for PIDDM using basis expansions. Specifically, we represent the state functions of the ODE model by cubic spline bases, assign a prior depending on ODE model fitting errors to basis coefficients, impose the Potts-model prior on cluster structures, and deliberately design a scaled ``spike-and-slab'' type of prior on indicators for significant directional effects. The ensuing joint