The art and science of simulation involves modeling the various possible events that could occur using random vectors. Further, in every study involving random vectors, the question of determining the dependence between the variables (in these vectors) is fundamental to the simulation and to the associated data processing techniques. In the simplest model, the variables can be viewed from a simplistic perspective, and assumed to be independent. At the other extreme of the spectrum, one can assume that every variable is dependent on every other variable. The situation then becomes both extremely complex and intractable unless one resorts to Markovian-like assumptions. In this paper, we shall show how one can model the dependence using a linear number of dependencies implying the so-called Dependence Tree. We shall discuss the various scenarios encountered when the metrics for measuring the quality of the approximation is entropy-based or Chi-square based. In each case, we shall show how one can simulate events based on such a random vector, and also how the parameters associated with this random vector can be learned. Experimental results demonstrating the power of this modeling strategy will are also included in the paper.

Dr. John Oommen was born in Coonoor, India on September 9, 1953. He obtained his B.Tech. degree from the Indian Institute of Technology, Madras, India in 1975. He obtained his M.E. from the Indian Institute of Science in Bangalore, India in 1977. He then went on for his M.S. and Ph. D. which he obtained from Purdue University, in West Lafayettte, Indiana in 1979 and 1982 respectively. He joined the School of Computer Science at Carleton University in Ottawa, Canada, in the 1981-82 academic year. He is still at Carleton and holds the rank of a Full Professor. Since July 2006, he has been awarded the honorary rank of Chancellor's Professor, which is a lifetime award from Carleton University. His research interests include Automata Learning, Adaptive Data Structures, Statistical and Syntactic Pattern Recognition, Stochastic Algorithms and Partitioning Algorithms. He is the author of more than 330 refereed book chapters, journal and conference publications, and is a Fellow of the IEEE and a Fellow of the IAPR. Dr. Oommen has also served on the Editorial Board of the IEEE Transactions on Systems, Man and Cybernetics, and Pattern Recognition.

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*Also an Adjunct Professor at the University of Agder in Grimstad, Norway.