A Polynomial Time Algorithm for Finding Bayesian Probabilities from
  Marginal Constraints
  A method of calculating probability values from a system of marginal
constraints is presented. Previous systems for finding the probability of a
single attribute have either made an independence assumption concerning the
evidence or have required, in the worst case, time exponential in the number of
attributes of the system. In this paper a closed form solution to the
probability of an attribute given the evidence is found. The closed form
solution, however does not enforce the (non-linear) constraint that all terms
in the underlying distribution be positive. The equation requires O(r^3) steps
to evaluate, where r is the number of independent marginal constraints
describing the system at the time of evaluation. Furthermore, a marginal
constraint may be exchanged with a new constraint, and a new solution
calculated in O(r^2) steps. This method is appropriate for calculating
probabilities in a real time expert system
