Factorization of Seperable and Patterned Covariance Matrices for Gibbs Sampling

Abstract – Recently the Gibbs sampler has become a very popular estimation tech-nique especially in Bayesian Statistics. In order to implement the Gibbs sampler, matrix factorizations must be computed which normally is not problematic. When the dimension of the matrices to be factored is large, computation time increases to an amount to merit spe-cial attention. I have found that when the matrices to be factored are separable or patterned, results from matrix theory can assist in computation time reduction