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 most basic 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. Although extensive experimental results demonstrating the power of this modeling/simulation strategy will be given in the formal presentation, this paper is necessarily brief.

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Keywords Dependence-Tree based modeling and simulation, Modeling random variables, Simulating random vectors
Conference 2010 Huntsville Simulation Conference, HSC 2010
Oommen, J. (2010). On utilizing Dependence-Tree modeling in arbitrary simulations. In Proceedings of the 2010 Huntsville Simulation Multiconference, HSC 2009 (pp. 247–250).