Combining knowledge from diverse sources: An alternative to traditional data independence hypotheses

Consider the assessment of any unknown event A through its conditional probability P(A \ B,C) given two data events B, C of different sources. Each event could involve many locations jointly, but the two data events are assumed such that the probabilities P(A \ B) and P(A \ C) can be evaluated. The challenge is to recombine these two partially conditioned probabilities into a model for P(A \ B,C) without having to assume independence of the two data events B and C. The probability P(A \ B,C) is then used for estimation or simulation of the event A. In presence of actual data dependence, the combination algorithm provided by the traditional conditional independence hypothesis is shown to be nonrobust leading to various inconsistencies. An alternative based on a permanence of updating ratios is proposed, which guarantees all limit conditions even in presence of complex data interdependence. The resulting recombination formula is extended to any number n of data events and a paradigm is offered to introduce formal data interdependence.