A sparse matrix approach to Bayesian computation in large linear models

Abstract

The problem of efficient Bayesian computation in the context of linear Gaussian directed acyclic graph models is examined. 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 Markov chain Monte Carlo algorithms with good mixing properties to be developed for problems with many thousands of latent variables.