Chapter 2 - Static Bayesian Networks:

Bayesian Networks in the Absence of

Temporal Information

Static Bayesian networks, or Bayesian networks are:

graphical models that allow a concise representation of the probabilistic dependencies

between a given set of random variables

X = {X1,X2, . . . ,Xp}

as a DAG G = (V,A) where each node corresponds to a random variable Xi.

2.1.1 Graph structure

Independence map - because there is no probabilistic independence, an Independence map (I-

map) is the probabilistic dependence structure P of X if there is a on-to-one correspondence

between the random variables in X and the nodes V of G

2.1.1 Fundamental connections

2.1.2 D- separation

V- structure: A and B are not independent given C

2.1.3 Equivalent structures.

Serial and diverging: A and B are independent

given C