Nonconjugate Bayesian analysis of variance component models

We consider the usual normal linear mixed model for variance components fro m a Bayesian viewpoint. With conjugate priors and balanced data, Gibbs samp ling is easy to implement; however, simulating from full conditionals can b ecome difficult for the analysis of unbalanced data with possibly nonconjug ate priors, thus leading one to consider alternative Markov chain Monte Car lo schemes. We propose and investigate a method for posterior simulation ba sed on an independence chain. The method is customized to exploit the struc ture of the variance component model, and it works with arbitrary prior dis tributions. As a default reference prior, we use a version of Jeffreys' pri or based on the integrated (restricted) likelihood. We demonstrate the ease of application and flexibility of this approach in familiar settings invol ving both balanced and unbalanced data.