Invariance and Bayesian predictive analysis with an application to the diallel cross design

The predictive approach to Bayesian inference is enriched with invariance considerations which naturally occur in experimental designs. Invariance is used extensively both to compute predictive distributions and to derive predictive models together with the posterior parameter distribution. Under the usual assumption of normality, a simple and direct relationship between predictive and posterior distribution is shown to exist. General results are illustrated in detail with reference to the diallel cross experimental design.