Shrink Large Covariance Matrix Without Penalty: An Empirical Nonparametric Bayesian Framework for Brain Connectivity Network Analysis

• Activity Number: 118
• Type: Topic Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Shuo Chen*+
• Companies: University of Maryland, College Park
• Keywords: Brain connectivity ; fMRI ; covariance ; shrinkage ; nonparametric Bayesian ; network

Abstract

In neuroimaging, brain connectivity generally refers to associations between neural units from distinct brain locations. For brain connectivity network analysis, we usually use nodes (vertices) to represent the neural processing units and edges to note connectivity between those units as in graph theory. The edge intensities (connectivity strengths) are often taken as input data. For statistical modeling, the covariance between edges yields important information because it not only reflect the correlation structure between edges also the spatial structure of nodes. However, the dimensionalty of covariance parameters is very high, for example, 300 nodes will lead to more than one billion covariance parameters between edges. Also, the correlations between edges within and out of brain networks show different distributions. We propose a novel empirical nonparametric Bayesian framework that can efficiently shrink the number of covariance parameters between edges with spatial structure constraint rather than penalty term and yield inferences of brain networks. We apply this method to an fMRI study and simulated data sets to demonstrate the properties of our method.