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Unit 8: Statistical Reasoning

 Adopt a model that can utilize a more local depiction to permit interactions among events Notes
that only affect each other.

 Some events may only be unidirectional others may be bidirectional — make a difference
between these in model.
 Events may be fundamental and so get chained jointly in a network.

8.3.1 Implementation

A Bayesian Network is define as a directed acyclic graph:

 A graph where the directions are links which specify dependencies that appears between
nodes.

 Nodes symbolize propositions regarding events or events themselves.
 Conditional probabilities measure the power of dependencies.

Example: Let us see the following example:

 The probability, P( ) that my car won’t begin.
1
 If my car won’t begin then it is possible that
 The battery is flat or
 The staring motor is broken.

To decide whether to fix the car myself or send it to the garage the following decision is made:
 If the headlights do not function then the battery is apt to be flat so i fix it myself.
 If the beginning motor is faulty then send car to garage.

 If battery and beginning motor both gone send car to garage.
The network to symbolize this is as follows:
Figure 8.1: A Simple Bayesian Network

Car wont start
Headlights not on
Battery flat Starting motor
defective

Replace battery Both wont work

Send car to garage

8.3.2 Reasoning in Bayesian Nets

 Probabilities in links follow typical conditional probability axioms.

 Thus follow links in attaining hypothesis and update beliefs consequently.

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