Block designs for random treatment effects

A Bayesian design criterion for selection experiments in plant breeding is derived using a utility function that minimizes the risk of an incorrect selection. A prior distribution on the heritability parameter is used to complete the definition of the design optimality criterion. An example is given with evaluations of the criterion for different prior distributions on the heritability. Though coming from a genetic motivation this criterion should prove useful for any other types of experiments with random treatment effects.