Variable elimination algorithm in Bayesian networks: An updated version

Given a Bayesian network relative to a set I of discrete random variables, we are interested in computing the probability distribution Pr(S), where the target S is a subset of I. The general idea of the Variable Elimination algorithm is to manage the successions of summations on all random variables out of the target. We propose a variation of the Variable Elimination algorithm that will make intermediate computation written as conditional probabilities and not simple potentials. This has an advantage in storing the joint probability as a product of conditions probabilities thus less constraining.