Covariance Partition Priors: A Bayesian Approach to Simultaneous Covariance Estimation

• Activity Number: 495
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Jeremy Gaskins*+ and Michael Daniels
• Companies: University of Florida and The University of Texas at Austin
• Keywords: longitudinal data ; clustering ; covariance estimation ; sparsity ; Bayesian methodology ; Cholesky parameterization

Abstract

The estimation of the covariance matrix is a key concern in the analysis of longitudinal data. When data consists of multiple groups, it is often assumed the covariance matrices are either equal across groups or are completely distinct. We seek methodology to allow for the borrowing of strength across potentially similar groups to improve estimation. We introduce a covariance partition prior which provides a partition of the groups at each measurement time. Groups in a common set of the partition share dependence parameters for the distribution of the current measurement given the preceding ones, and the sequence of partitions is modeled as Markov chain to encourage them to vary smoothly across measurement times. This approach additionally encourages a lower-dimensional structure of the covariance matrices by using a sparse Cholesky structure. We demonstrate the performance of our model through a simulation study and analysis of data from a depression study.