Exact Propagation in Probabilistic Network Models

In the previous chapters we presented and discussed different methodologies for building a coherent and consistent knowledge base for a probabilistic expert system. The knowledge base of a probabilistic expert system includes the joint probability distribution (JPD) for the variables involved in the model. Once the knowledge base has been defined, one of the most important tasks of an expert system is to draw conclusions when new information, or evidence, is observed. For example, in the field of medical diagnosis, the main task of an expert system consists of obtaining a diagnosis for a patient who presents some symptoms (evidence). The mechanism of drawing conclusions in probabilistic expert systems is called propagation of evidence,[1] or simply propagation. Propagation of evidence consists of updating the probability distributions of the variables according to the newly available evidence. For example, we need to calculate the conditional distribution of each element of a set of variables of interest (e.g., diseases) given the evidence (e.g., symptoms).