Theory

Theory 1

Bayes’ Theorem

For any events and :

Note: Bayes’ Theorem is sometimes called Bayes’ Rule.

Bayes’ Theorem - Derivation

Start with the observation that , in other words event “ AND ” equals event “ AND ”.

Apply the multiplication rule to each product:

Equate them and rearrange:

The main application of Bayes’ Theorem is to calculate when it is easy to calculate from the problem setup. Often this occurs in multi-stage experiments where event describes outcomes of an intermediate stage.

Note: These lecture notes use alphabetical order , as a mnemonic for temporal or logical order, i.e. that comes first in time, or that is the prior conditional from which it is easy to calculate .