Probabilistic graphical models

Abstract

This chapter discusses defining a model over its whole set of variables by the composition of a number of sub-models each involving only fewer variables. It focuses on the kind of composition induced by independence relations among the variables. Graphs are particularly suitable for the modelling of such independencies; the chapter formalizes the discussion within the framework of probabilistic graphical models. The chapter describes a class of probabilistic graphical models with imprecision based on directed graphs called credal networks (CNs). CNs are regarded as a generalization to imprecise probabilities of Bayesian networks. With respect to these precise probabilistic graphical models, CNs should be regarded as a more expressive class of models.