Write the complete joint probability formula for the following Bayesian network.

Question

joint probability formula for Bayesian network

For the given Bayesian Network, the joint probability has to be found. Since the probabilities are not specified, just a formula is written.

The joint probability formula for the given Bayesian Network is:

P(A,B,C,D,E) = P(E|A,B,C) P(A|D) P(B|A) P(D|C) P(C)

A Bayesian network consists of a set of directed edges that connect a set of variables.

Each variable will have a finite set of states which are mutually exclusive.

The variables and directed edges form a directed acyclic graph (DAG).

In the given BN, the probabilities to be specified are:

P(E|A,B,C)

P(A|D)

P(B|A)

P(D|C)

P(C)

The above probabilities for the variables are based on the incoming edge.

The joint probability of a general Bayesian network can be written as:

The joint probability for the given Bayesian Network can be written as:

P(A,B,C,D,E) = P(E|A,B,C) P(A,B,C,D)

= P(E|A,B,C) P(A|D) P(B|A) P(D,C)

= P(E|A,B,C) P(A|D) P(B|A) P(D|C) P(C)

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