Bayesian Networks, with example.

    ·          It is a DS which is a graph, in which each node is annotated with quantitative probability information.

·         The nodes and edges in the graph are specified as follows –

1.   A set of random variables make up the nodes of the network. These variables may be discrete or continuous.

2.   A set of directed links or arrows connects pairs of nodes. If there is an arrow from node X to node Y, then X is said to be a parent of Y.

3.   Each node Xi has a conditional probability distribution that quantifies the effect of the parents on the node.

4.   The graph has no directed cycles.

 ·    The set of nodes and links is called the topology of the network.

     ·    The topology specifies the conditional independence relationships that hold in the domain.

     ·    Once the Bayesian network topology is specified, the conditional probability distribution for each variable is specified.

 ·     For this, its parent information is required.

 ·     Ex.: