Biology Reference
In-Depth Information
Chapter 2
Bayesian Networks in the Absence of Temporal
Information
Abstract
Data recorded across multiple variables of interest for a given
phenomenon often do not contain any explicit temporal information. In the absence
of such information, the data essentially represent a static snapshot of the underly-
ing phenomenon at a particular moment in time. For this reason, they are sometimes
referred to as
static data
.
Static Bayesian networks, commonly known simply as Bayesian networks, pro-
vide an intuitive and comprehensive framework to model the dependencies between
the variables in static data. In this chapter, we will introduce the essential defini-
tions and properties of static Bayesian networks. Subsequently, we will discuss ex-
isting Bayesian network learning algorithms and illustrate their applications with
real-world examples and different
R
packages.
2.1 Bayesian Networks: Essential Definitions and Properties
Bayesian networks are a class of
graphical models
that allow a concise represen-
tation of the probabilistic dependencies between a given set of random variables
X
=
{
X
1
,
X
2
,...,
X
p
}
as a
directed acyclic graph
(DAG)
G
=(
V
,
A
)
. Each node
v
i
∈
V
corresponds to a random variable
X
i
.
2.1.1 Graph Structure and Probability Factorization
The correspondence between the graphical separation (
⊥
G
) induced by the absence
of a particular arc and probabilistic independence (
⊥
P
) provides a convenient way
to represent the dependencies between the variables. Such a correspondence is for-
mally known as an
independency map
(
Pearl
,
1988
) and is defined as follows.
Definition 2.1 (Maps).
Agraph
G
is an
independency map
(I-map) of the proba-
bilistic dependence structure
P
of
X
if there is a one-to-one correspondence between
Search WWH ::
Custom Search