14.1 The Bayesian Network Formalism 333
Figure 14.1 Example of a BN for medical diagnosis. Rectangles represent discrete
random variables and the oval represents a continuous random variable.
- Flu, meaning that a patient has influenza.
- Cold, meaning that a patient has one of a number of milder respiratory
infections. - Perceives Fever (PF), meaning that the patient perceives that he or she has
a fever. - Temperature, the continuous random variable representing a measure-
ment of the patient’s body temperature.
Note that three of the random variables are Boolean, the simplest kind of
discrete random variable, and that the fourth random variable is continuous.
Two of the nodes have no incoming edges, so their CPDs are just PDs, and be-
cause the nodes are Boolean, they can be specified with just one probability.
We assume thatPr(Flu)=0. 0001 , corresponding to the fact that the annual
incidence rate for influenza (serious enough to require hospitalization) in the
United States was 1.0 per 10,000 in 2002 (NCHS 2003). The common cold
is much more common. We will usePr(Cold)=0. 01 , although the actual
incidence rate is higher than this.
The CPD for the PF node has two incoming edges, so its CPD is a table that
gives a conditional probability for every combination of inputs and outputs.
For example, the CPD might be the following: