14 Bayesian Networks
Stochastic modeling has a long history, and it is the basis for the empiri-
cal methodology that has been used with great success by modern scien-
tific disciplines. Stochastic models have traditionally been expressed using
mathematical notation that was developed long before computers and GUIs
became commonly available. A Bayesian network (BN) is a graphical mecha-
nism for specifying the joint probability distribution (JPD) of a set of random
variables (Pearl 1998). As such, BNs are a fundamental probabilistic repre-
sentation mechanism for stochastic models. The use of graphs provides an
intuitive and visually appealing interface whereby humans can express com-
plex stochastic models. This graphical structure has other consequences. It is
the basis for an interchange format for stochastic models, and it can be used
in the design of efficient algorithms for data mining, learning, and inference.
The range of potential applicability of BNs is large, and their popularity
has been growing rapidly. BNs have been especially popular in biomedical
applications where they have been used for diagnosing diseases (Jaakkola
and Jordan 1999) and studying complex cellular networks (Friedman 2004),
among many other applications.
This chapter divides the subject of BNs into three sections. The sections
answer three questions: What BNs are, How BNs are used, and How BNs
are constructed. The chapter begins with the definition of the notion of a BN
(section 14.1). BNs are primarily used for stochastic inference, as discussed
in section 14.2. BNs are named after Bayes because of the fundamental im-
portance of Bayes’ law for stochastic inference. Because BNs require one to
specify probability distributions as part of the structure, statistical methods
will be needed as part of the task of constructing a BN. Section 14.3 gives an
overview of the statistical techniques needed for constructing and evaluating
BNs.
