Received: 29 September 2016 Revised: 24 January 2017 Accepted: 7 March 2017 DOI: 10.1111/coin.12130 ORIGINAL ARTICLE On a simple method for testing independencies in Bayesian networks Cory J. Butz 1 André E. dos Santos 1 Jhonatan S. Oliveira 1 Christophe Gonzales 2 1 Department of Computer Science, University of Regina, Regina, Canada 2 LIP6 - dpartement DESIR, Universit Pierre et Marie Curie, Paris, France Correspondence Cory J. Butz, Department of Computer Science, University of Regina, Regina, Saskatchewan, Canada. Email: Butz@cs.uregina.ca Funding information NSERC Discovery, Grant/Award Number: 238880 Abstract Testing independencies is a fundamental task in reason- ing with Bayesian networks (BNs). In practice, d-separation is often used for this task, since it has linear-time com- plexity. However, many have had difficulties understanding d-separation in BNs. An equivalent method that is easier to understand, called m-separation, transforms the problem from directed separation in BNs into classical separation in undirected graphs. Two main steps of this transformation are pruning the BN and adding undirected edges. In this paper, we propose u-separation as an even simpler method for testing independencies in a BN. Our approach also converts the problem into classical separation in an undirected graph. However, our method is based upon the novel con- cepts of inaugural variables and rationalization. Thereby, the primary advantage of u-separation over m-separation is that m-separation can prune unnecessarily and add superfluous edges. Our experiment results show that u-separation performs 73% fewer modifications on average than m-separation. KEYWORDS Bayesian networks, d-separation, m-separation, testing independencies 1 INTRODUCTION Pearl 1 states that perhaps the founding of Bayesian networks (BNs) 2-4 made its greatest impact through the notion of d-separation. d-Separation 5 is a graphical method for deciding which conditional inde- pendence relations are implied by the directed acyclic graph (DAG) of a BN. To test whether 2 sets X and Z of variables are conditionally independent given a third set Y of variables, denoted I(X, Y, Z), d-separation checks whether every path from X to Z is “blocked” by Y in the DAG. d-Separation Computational Intelligence. 2017;1–13. wileyonlinelibrary.com/journal/coin © 2017 Wiley Periodicals, Inc. 1