A branch-and-bound method for finding independently distributed probability models that satisfy probability order constraints

A branch-and-bound method for finding independently distributed probability models is presented. Such models attempt to capture expert preference by (inequality) order relationships and are useful for the development of decision support systems. Finding probability models with independent distributions can be formulated as a linear-constraint optimization problem with a dynamic cost function. A simplex-like algorithm was implemented for branching and bounding between two search spaces on finding the desired models. In these two search spaces, one encompasses all possible independent probability distributions, while the other encompasses all distributions that satisfy all probability order constraints.