2.4 Posterior probability model

The posterior probability model is defined as: \(P(\text{is fake | has !})\) and \(P(\text{is real | has !})\)

and this can be calculated using Bayes’ Rule:

\[ \text{posterior} = \frac{\text{prior} \times \text{likelihood}}{\text{normalizing constant}} \]

	Fake	Real
prior	40.0%	60.0%
likelihood	26.7%	2.2%
posterior	88.9%	11.1%

Shortcut to calculating the normalizing constant:

\[ \text{normalising constant} = \text{sum}(\text{prior} \times \text{likelihood}) \]