A Note on Bayesian Design for the Normal Linear Model with Unknown Error Variance

The Bayesian theory of optimal experimental design for the normal linear model has been developed under the assumption of known variance. The insensitivity of specific design criteria to prior assumptions on the variance distribution has been demonstrated in special cases, but a general result showing the way in which Bayesian optimal designs are affected by prior information on the variance is lacking. This note proves that Bayesian designs are insensitive to information about the variance in a more general way than previously thought.