Bayesian Estimation of Block Covariance Matrices

We develop estimation methods for Bayesian models where the covariance matrix has a block structure. A block covariance matrix partitions the data into groups or blocks; variances and covariances are equal within blocks while covariances are equal across blocks. We derive the posterior and marginal likelihood for a Gaussian regression model when the number of blocks and the assignment of each series to a block are known. When the block structure is unknown, we build a random partition model which assigns a prior distribution over the space of partitions of the data into blocks. We develop Monte Carlo sampling algorithms that search model space over the different ways the covariance matrix can be partitioned into blocks