Bayesian parsimonious covariance estimation for hierarchical linear mixed models

We consider a non-centered parameterization of
the standard random-effects model, which is based on the
Cholesky decomposition of the variance-covariance matrix.
The regression type structure of the non-centered parameterization
allows us to use Bayesian variable selection methods
for covariance selection. We search for a parsimonious
variance-covariance matrix by identifying the non-zero elements
of the Cholesky factors. With this method we are
able to learn from the data for each effect whether it is random
or not, and whether covariances among random effects
are zero. An application in marketing shows a substantial
reduction of the number of free elements in the variance-covariance matrix.