Semantics Of Bayesian Networks

Introduction to Bayesian Network:

Lot of domain question can be answered by the joint probability distribution, but it become hard to control when number of variable increase. In fact specifying probability for atomic event requires a large amount of data and cannot be done when they are not sufficient

For the fully joint distribution the individual probability of variables are needed but their independence and conditional independence among each other can greatly reduce their probabilities. So here the Bayesian Network, a type of data structure comes into the picture, which is used as a better method to represent dependencies among variables and specify more briefly any full joint probability distribution

This in fact, is, another method used to reduce the complexity of certainty factor. A directed graph is used where each of the node are annotated with the amount fo probability information.

Semantics of Bayesian Networks:

Bayesian networks can be visualize in two ways:

1. The network as the representation of joint probability distribution. This help us to understand how the network can be constructed.

2. Visualize the networks as an encoding of a number of conditional independence statements. This is neat and convenient in designing inference procedures. However, the two ways are similar and identical.

Representing the Full Joint Distribution:

Lets consider example from the chapter Bayesian Networks

We explain it, by calculating the probability that the alarm has sounded, but neither the burgulary nor an earthquake has occurred, and both John and Mary telephone you.

This can be generalize as below:

where parents (x) denotes the specific values of the variables in the parents (x).

If the Bayesian network is a representation of the joint distribution then it too can be used to answer any query, as earlier in the case of inference through probabilities. This does it really so and that too more efficiently. An extension of Bayesian network is called Decision Net Work or Influence Diagram.