  Problems of probabilistic inference and decision making under uncertainty
commonly involve continuous random variables. Often these are discretized to a
few points, to simplify assessments and computations. An alternative
approximation is to fit analytically tractable continuous probability
distributions. This approach has potential simplicity and accuracy advantages,
especially if variables can be transformed first. This paper shows how a
minimum relative entropy criterion can drive both transformation and fitting,
illustrating with a power and logarithm family of transformations and mixtures
of Gaussian (normal) distributions, which allow use of efficient influence
diagram methods. The fitting procedure in this case is the well-known EM
algorithm. The selection of the number of components in a fitted mixture
distribution is automated with an objective that trades off accuracy and
computational cost.
