Bayesian Estimation of Means for the Random Effect Model

The problem of estimating the means in the one-way random effect model yjk = θj+ejk is considered from a Bayesian viewpoint. Posterior distributions of the θj are obtained under the assumption that the θj are independently drawn from a Normal population N(θ, σ22) and that the ejk are independent random errors having a N(0, σ21) distribution. It is shown that the posterior distributions of the θj are clustered more closely together than are the corresponding distributions for a fixed effect model. A numerical example is given.