Testing of Multialternative Hypotheses under a Priori Uncertainty

An optimal decision rule for testing multialternative hypotheses is constructed for the case where the available information about the a priori probability distribution is limited to knowledge of the admissible region of probability values. The optimality criterion is minimax deviation of the mean risk from the Bayesian risk for a known a priori distribution of the hypotheses. General expressions are derived for the maximum deviation, the structure of the optimal decision rule is determined, and relationships for the choice of decision rule parameters are established. Some examples are considered, many of which produce an optimal decision rule for a whole class of practical problems.