# Bayesian Networks, Introduction and Practical Applications

Wim Wiegerinck, Willem Burgers, and Bert Kappen

Abstract. In this chapter, we will discuss Bayesian networks, a currently widely accepted modeling class for reasoning with uncertainty. We will take a practical point of view, putting emphasis on modeling and practical applications rather than on mathematical formalities and the advanced algorithms that are used for computation. In general, Bayesian network modeling can be data driven. In this chapter, however, we restrict ourselves to modeling based on domain knowledge only. We will start with a short theoretical introduction to Bayesian networks models and inference. We will describe some of the typical usages of Bayesian network models, e.g. for reasoning and diagnostics; furthermore, we will describe some typical network behaviors such as the explaining away phenomenon, and we will briefly discuss the common approach to network model design by causal modeling. We will illustrate these matters by a detailed modeling and application of a toy model for medical diagnosis. Next, we will discuss two real-world applications. In particular we will discuss the modeling process in some details. With these examples we also aim to illustrate that the modeling power of Bayesian networks goes further than suggested by the common textbook toy applications. The first application that we will discuss is for victim identification by kinship analysis based on DNA profiles. The distinguishing feature in this application is that Bayesian networks are generated and computed on-the-fly, based on case information. The second one is an application for petrophysical decision support to determine the mineral content of a well based on borehole measurements. This model illustrates the possibility to model with continuous variables and nonlinear relations.