Quite frequently diagnosis is not final with one medical test but a sequence of tests are applied. How the information given by one test is going to be combined with the information conveyed by a second test? Can we ”add up” the information of the medical tests assuming conditional independence that is the ”independence”or ”naive” Bayes? In this article we develop a very simple and basic exact Bayes Factor to check the independent Bayes Model VS the full Bayes Model, without the assumption of conditional independence. Assuming independence Bayes when in fact is not, overstate the accumulation of two positives in favor of the disease and two negatives against. Here we also illustrate, that even in situations of mild evidence against the independence model the difference between the two models may be strikingly different in the presence of conflicting evidence between the medical tests. As a practical advice, when a sequence of tests are applied in combination routinely, a study should be conducted for which the joint results of a set of patients is kept and studied with and without the assumption of independence Bayes and Bayes Factors should be calculated. This work extends and generalizes the work of Pereira and Pericchi (1990) and Berger and Moosman (2001).
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