Covariance Partition Priors: A Bayesian Approach to Simultaneous Covariance Estimation for Longitudinal Data
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 borrowing of strength across potentially similar groups to improve estimation.  We introduce a covariance partition prior which proposes a partition of the groups at each measurement time.  Groups in the same 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 a Markov chain to encourage similar structure at nearby measurement times.This approach additionally encourages a lower-dimensional structure of the covariance matrices by shrinking the parameters of the Cholesky decomposition toward zero.  We demonstrate the performance of our model through two simulation studies and the analysis of data from a depression study.

Bio: Jeremy Gaskins is Assistant Professor in the Department of Bioinformatics & Biostatistics at the University of Louisville, where he has been since 2013.  He earned a B.S. in Mathematics and Applied Mathematics from Auburn University in 2007.  In 2013 he completed a Ph.D. in Statistics from the University of Florida, writing his dissertation on Bayesian estimation of dependence structures in longitudinal data.  His research interests include longitudinal data, simultaneous covariance estimation, correlation structures, missing data models, and Markov chain Monte Carlo methodology.