ABSTRACT
The main goal of this chapter is to describe a new method for representing and solving Bayesian decision problems. A new representation of a decision problem called a valuation-based system is described. A graphical depiction of a valuationbased system is called a valuation network. Valuation networks are similar in some respects to influence diagrams. Like influence diagrams, valuation networks are a compact representation emphasizing qualitative features of symmetric decision problems. Also, like influence diagrams, valuation networks allow representation of symmetric decision problems without any preprocessing. But there are some differences. Whereas influence diagrams emphasize conditional independence among random variables, valuation networks emphasize factorizations of joint probability distributions. Also, the representation method of influence diagrams allows only conditional probabilities. While conditional probabilities are readily available in pure causal models, they are not always readily available in other graphical models (see, for example, Darroch ei al, 1980; Wermuth and Lauritzen, 1983; Edwards and Kreiner, 1983; Kiiveri et al, 1984; Whittaker, 1990). The representation method of valuation-based systems is more general and allows direct representation of all probability models.
