These are the graphical structures used to represent the probabilistic relationship among a set of random variables. Bayesian networks are also called Belief Networks or Bayes Nets. BNs reason about uncertain domain.
In these networks, each node represents a random variable with specific propositions. For example, in a medical diagnosis domain, the node Cancer represents the proposition that a patient has cancer.
The edges connecting the nodes represent probabilistic dependencies among those random variables. If out of two nodes, one is affecting the other then they must be directly connected in the directions of the effect. The strength of the relationship between variables is quantified by the probability associated with each node.
There is an only constraint on the arcs in a BN that you cannot return to a node simply by following directed arcs. Hence the BNs are called Directed Acyclic Graphs (DAGs).
BNs are capable of handling multivalued variables simultaneously. The BN variables are composed of two dimensions −
● Range of prepositions
● Probability assigned to each of the prepositions.
Consider a finite set X = {X1, X2, …,Xn} of discrete random variables, where each variable Xi may take values from a finite set, denoted by Val(Xi). If there is a directed link from variable Xi to variable, Xj, then variable Xi will be a parent of variable Xj showing direct dependencies between the variables.
The structure of BN is ideal for combining prior knowledge and observed data. BN can be used to learn the causal relationships and understand various problem domains and to predict future events, even in case of missing data.