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DEVELOPMENT OF A GENERAL THEORY
PROPERTIES OF BAYES SOLUTIONS WHEN
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absolutely continuous ad inf assigns the probability Assumptions 3.1 Bayes solution relative bounded function chance variables Xi Chapter class of decision Clearly corresponding cost of experimentation decision function decision problem defined denote the probability denotes the decision denumerable subset discrete probability measures distribution functions element F equal equation experimentation is carried favorable a priori finite number finite subset follows from Theorem game is strictly game relative Hence Infj interval estimation intrinsic metric least favorable Lebesgue measure Lemma liminf measure zero minimal complete class minimax solution minimax strategy mixed strategies number of observations open subset positive integer priori distribution priori probability measure Proof pure strategies regular convergence restricted risk risk function sample xi satisfies Section set-theoretical sum single stage space Dl stochastic process strategy of player strictly determined terminal decision theory tion true distribution uniformly better weight function