A sparse matrix approach to Bayesian computation in large linear models

This paper examines the problem of efficient Bayesian computation in the context of linear Gaussian Directed Acyclic Graph (DAG) models. Unobserved latent variables are grouped together in a block, and sparse matrix techniques for computation are explored. Conditional sampling and likelihood computations are shown to be straightforward using a sparse matrix approach, allowing MCMC algorithms with good mixing properties to be developed for problems with many thousands of latent variables.