Bayesian estimates in a one-way ANOVA random effects model

Abstract

Bayesian estimators of variance components are developed, based on posterior mean and posterior mode, respectively, in a one-way ANOVA random effects model with independent prior distributions. The formulas for the proposed estimators are simple. The estimators give sensible results for 'badly-behaved' datasets, where the standard unbiased estimates are negative. They are markedly robust as compared to the existing estimators such as the maximum likelihood estimators and the maximum posterior density estimators.