Measuring conformability of probabilities

Given a probability space or a joint distribution, any derived probabilities or marginal distributions will be conformable. The inverse problem is to determine whether a set of fragmentary probabilities or marginal distributions is conformable in the sense that there exists a probability space or joint distribution that yields these fragmentary probabilities or marginal distributions. Because nonconformability or inconsistency may occur in a number of ways, we present a hierarchy of inconsistencies, and provide a linear programming approach designed to uncover different levels of inconsistency.