for incorporating different views of genomic data. Here, we give a brief introduc-
tion to BNs followed by a review of applications in biological data integration.
A Bayesian networkis a directed acyclic graph (DAG), where each node
represents a random variable, while edges between the nodes represent probabilistic
dependencies between the corresponding random variables.^105 Directions of edges
indicate the conditional dependence between variables. For a simple explanation,
consider the following toy example of a Bayesian network shown in Fig. 3. Four
random variables,X 1 ,X 2 ,X 3 ,andX 4 , representing genes’expression levels, are
related via conditional probabilities. In this case, we only considerdiscretegene
states; therefore, a gene might be expressed (on) or not (off). This is an example of
discrete BN where conditional probabilities are often given in the form of Condi-
tional Probability Tables (CPTs), shown next to each node in Fig. 3. Continuous BN
may also be modeled, but instead of CPTs, we use conditional probability densities
to represent relations between variables. Each variable in the BN representation
depends on the states of itsparents. For instance, in this case, the prognosis
variable,X 5 , which may model the clinical outcome, has two parents: gene 3 and
gene 4 (i.e., variableX 3 andX 4 ). The measure of dependency ofX 5 onX 3 andX 4 is
the conditional probabilityP(X 5 |X 3 ,X 4 ). The small number of parents for each
Fig. 3 A toy example of a Bayesian network with five binary variables. The conditional proba-
bilities are shown next to each variable
(^105) Ben-Gal ( 2007 ).
158 V. Gligorijevic ́and N. Pržulj