ABSTRACT
This chapter introduces probabilities, belief functions, and graphical models, showing how they form an extensive tool kit for building models about complex relationships among a large collection of attributes (or variables). The class of valuations allows one to think about both belief function and probabilistic models in a uniform framework. The chapter looks at representing probabilities in terms of potentials, and describes low-parameter representations of probabilities using groupings of outcomes together which simplify elicitation. A probabilistic graphical model is composed of two different sorts of valuations: unconditional probabilities and conditional probabilities. In order to fit the probability potentials into the valuation framework, one must define the combination (consisting of convolution and normalization) and projection (consisting of marginalization and extension) operators and provide an interchange theorem. To marginalize out a variable in a probability distribution in potential form simply sum over the dimension of the array corresponding to the dropped variables.
