International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 845398, 13 pages
doi:10.1155/2011/845398
Research Article

Uniqueness of the Level Two Bayesian Network Representing a Probability Distribution

New York Institute of Technology, College of Arts and Sciences, P.O. Box 840878, Amman 11184, Jordan

Received 29 June 2010; Accepted 8 November 2010

Academic Editor: Hana Sulieman

Copyright © 2011 Linda Smail. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Bayesian Networks are graphic probabilistic models through which we can acquire, capitalize on, and exploit knowledge. they are becoming an important tool for research and applications in artificial intelligence and many other fields in the last decade. This paper presents Bayesian networks and discusses the inference problem in such models. It proposes a statement of the problem and the proposed method to compute probability distributions. It also uses D-separation for simplifying the computation of probabilities in Bayesian networks. Given a Bayesian network over a family 𝐼 of random variables, this paper presents a result on the computation of the probability distribution of a subset 𝑆 of 𝐼 using separately a computation algorithm and D-separation properties. It also shows the uniqueness of the obtained result.