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A Rule for the Integration of Bayesian Opinions1

A rule is derived for the integration of probabilistic opinions. Each opinion is taken to be the output of a Bayesian processor which attaches a posteriori probabilities to the possible states of nature (hypotheses). Each processor is assumed to interpret a single independent component of a multidimensional input datum. The rule combining the several opinions is realized in a straightforward multiplicative algorithm which corrects for the redundancy of the a priori probabilities in each processor. The scheme is discussed in relation to implications for man-machine diagnosis in dispersed decision systems.