Bayesian Network Inference Algorithms - Bayesian Networks in R: With Applications in Systems Biology - page 84

Chapter 4
Bayesian Network Inference Algorithms
Abstract Chapters 2 and 3 discussed the importance of learning the structure and
the parameters of Bayesian networks from observational and interventional data
sets. Bayesian inference on the other hand is often a follow-up to Bayesian net-
work learning and deals with inferring the state of a set of variables given the state
of others as evidence. Such an approach eliminates the need for additional experi-
ments and is therefore extremely helpful. In this chapter, we will introduce inferen-
tial techniques for static and dynamic Bayesian networks and their applications to
gene expression profiles.
4.1 Reasoning Under Uncertainty
Bayesian networks, like other statistical models, can be used to answer questions
about the nature of the data that go beyond the mere description of the observed
sample. Techniques used to obtain those answers based on new evidence are known
in general as inference . For Bayesian networks, the process of answering these
questions is also known as probabilistic reasoning or belief updating , while the
questions themselves are called queries . Both names were introduced by Pearl
( 1988 ) and borrowed from expert systems theory (e.g., you would submit a query
to an expert to get an opinion and update your beliefs accordingly) and have com-
pletely replaced traditional statistical terminology in recent works such as Koller
and Friedman ( 2009 ).
4.1.1 Probabilistic Reasoning and Evidence
In practice, probabilistic reasoning on Bayesian networks has its roots embedded
in Bayesian statistics and focuses on the computation of posterior probabilities
or densities. For example, suppose we have learned a Bayesian network B with