Bayesian Hierarchical Modeling on Covariance Valued Data

• Activity Number: 162 - SBSS Student Paper Award Session - I
• Type: Topic Contributed
• Date/Time: Monday, July 29, 2019 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Satwik Acharyya* and Zhengwu Zhang and Anirban Bhattacharya and Debdeep Pati
• Companies: Texas A&M University and University of Rochester Medical Center and TAMU and Texas A&M University
• Keywords: Change Point; Covariance Matrix; Functional Connectivity; Low Rank; Stiefel Manifold; Wishart Distribution

Abstract

Analysis of functional connectivity of human brains is of pivotal importance for diagnosis of cognitive ability. The Human Connectome Project(HCP) provides an excellent source of neural data across different regions of human brain. Individual specific data were available (Dai et al., 2015) in the form of time varying covariance matrices representing the brain activity as the subjects perform a specific task. As a preliminary objective of studying the heterogeneity of brain connectomics across the population, we develop a probabilistic model for a sample of covariance matrices using a scaled Wishart distribution. Based on empirical explorations suggesting the data matrices to have low effective rank, we further model the center of the Wishart distribution using an orthogonal factor model type decomposition. We encourage shrinkage towards a low rank structure through a novel shrinkage prior and discuss strategies to sample from the posterior distribution using a combination of Gibbs and slice sampling. We extend our modeling framework to a dynamic setting to detect change points. The efficacy rates are explored through simulation settings and case studies including HCP data.