Testing system entropy and prediction error probability

Composite hypotheses concerning stochastic system entropy, are considered. Asymptotically α-level tests for statistical testing of these hypotheses against their alternatives are derived. For the most interesting cases (extremely small and extremely large entropies) the critical regions are explicitely calculated. It is shown that these tests can be used for testing the probability of error of the Bayes predictor of the system states. The method is illustrated by testing the system stability and by testing optimality of a medical diagnosis expert system. The main attention is focused on Shannon entropies, but alternative entropies are also considered