Robust Bayesian Methods in Simple ANOVA Models

We develop a robust Bayesian inference procedure for the simple analysis of variance (ANOVA) model. In the ANOVA model of a two-way layout crossover study, the problem of partial prior robustness can be reduced to componentwise variations of positive-definite diagonal matrices. The feasible ellipsoid (a hyperinterval), the intersection, and the union of HPD regions (HiFi region) are derived.