Abstract : This thesis is designed to develope a new algorithm to compute marginal and conditional probabilities in bayesian networks. In chapter 1 we present the theory of bayesian networks. We introduce a new concept, the one of bayesian network of level two, which is a new key method to introduce our computation algorithm. In chapter 2, we present a graphical property called "D-separation" which allows to determine, for any couple of random variables, and any set of conditioning, if there is, or not, conditional independence. We also present results related to the computation of probability and conditional probabilities in the bayesian networks by using the properties of d-separation. In chapter 3 we give the presentation and the justification of one of the known algorithms of computation in the bayesian networks : the LS algorithm (Lauritzen and Spiegelhalter), based on the method of junction tree. In addition, after having presented the concept of proper covering sequence
with the running intersection property, we propose an algorithm in two versions (of which one is new) which allows to build a succession of parts of a bayesian network having this property. In chapter 4, we develope the successive restrictions algorithm which we propose for the computation of probabilities (in its first version) and of conditional probabilities (in its second version).