An efficient monotone data augmentation algorithm for Bayesian analysis of incomplete longitudinal data

We introduce a new method for sampling from the Wishart distribution by representing the Wishart distributed random matrix as a function of independent multivariate normal-gamma random vectors. An efficient monotone data augmentation (MDA) algorithm is developed for Bayesian multivariate linear regression. For longitudinal outcomes, the proposed method is easier to implement and interpret than that based on Bartlett’s decomposition. The proposed algorithm is illustrated by the analysis of an antidepressant trial.