Abstract
This paper deals with optimum information processing problems in the general setting of decision problems. Information structures are described by σ-fields generated by data and structures of transition probability. From the intrinsic standpoint of decision problems, the information value induced by the optimum objective cost functional is defined. From the standard information theory, an information measure such as Shannon's mutual information is introduced. Relations among information structures, the information value and the information measure are clarified. Using these results, optimum design problems of information structures with respect to the information value are discussed. Further, a new design method is proposed, which is not directly based on the information value, namely the objective cost functional, but on the information measure. It is however shown that this method is not inconsistent with the information value and has a simple form.
