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Problems of probabilistic inference and decision making under uncertaintycommonly involve continuous random variables. Often these are discretized to afew points, to simplify assessments and computations. An alternativeapproximation is to fit analytically tractable continuous probabilitydistributions. This approach has potential simplicity and accuracy advantages,especially if variables can be transformed first. This paper shows how aminimum relative entropy criterion can drive both transformation and fitting,illustrating with a power and logarithm family of transformations and mixturesof Gaussian (normal) distributions, which allow use of efficient influencediagram methods. The fitting procedure in this case is the well-known EMalgorithm. The selection of the number of components in a fitted mixturedistribution is automated with an objective that trades off accuracy andcomputational cost.

Mixtures of Gaussians and Minimum Relative Entropy Techniques for Modeling Continuous Uncertainties