ABSTRACT
This chapter introduces a Bayesian analysis of the mixed model. The mixed model is more general than the fixed because in addition to containing fixed effects the model contains so called random effects. The random factors of the model are unobservable random variables and these have variances called variance components which are the primary parameters of interest. The chapter explores joint and marginal posterior distributions for the parameters. The posterior distribution of b is a key factor in obtaining the conditional distribution of the variance components as well as determining the posterior marginal distribution of these parameters. The distribution of b is very difficult to handle, thus one way of solving the problem is to find an approximation in terms of simple expressions. A way to estimate the parameters of mixed linear models is with the mode of the joint posterior distribution of all the parameters.
