In this paper we give a simple account of local computation of marginal probabilities for when the joint probability distribution is given in factored form and the sets of variables involved in the factors form a hypertree. Previous expositions of such local computation have emphasized conditional probability. We believe this emphasis is misplaced. What is essential to local computation is a factorization. It is not essential that this factorization be interpreted in terms of conditional probabilities. The account given here avoids the divisions required by conditional probabilities and generalizes readily to alternative measures of subjective probability, such Dempster-Shafer or Spohnian belief functions.
Shafer, G. R. and P. P. Shenoy, "Probability Propagation," Annals of Mathematics and Artificial Intelligence, Vol. 2, Nos. 1--4, 1990, pp. 327--351.