ABSTRACT
In this chapter, the authors explain how to do computations in a two-node Bayesian Network (BN). They show how Bayes' theorem can be extended to perform the necessary probability updating when the authors consider an extended version of the problem. The authors demonstrate how the underlying idea of Bayesian "propagation" through the network provides some very powerful types of reasoning. They describe the basic structural properties of BNs, and outline recognition of these properties that form the basis for the general propagation algorithm. The authors show how BNs can be used to "solve" the Monty Hall problem and Simpson's paradox. They cover the atomic fragments of BNs, in the form of d-connection types. These support modeling multiple causes, multiple consequences, and explaining away, an operation that is central to human reasoning about uncertainty. A number of algorithms use variable elimination, or variants thereof, for computation in BNs.
