A posteriori integration of probabilities. Elementary theory (Q2790680)

In socio-economic and environmental studies of complex poorly observable systems, certain specific properties of objects under study are used to synthesize or integrate unmatched observations. In this article, the author proposes a unified approach to the integration of a priori distributions given by independent sources in the absence of any prioritization of the sources by reliability. The proposed approach is based on the notion of an a posteriori event in the product of probability spaces corresponding to the a priori probabilities. A max measure of concentration is defined which gives the comparison of informativeness of a priori and a posteriori probabilities. Algebraic properties of a posteriori integration is studied as a binary operation on the set of probabilities. Studies of asymptotic behaviour of the results of a posteriori integration of infinite probability sequences are outlined.