Bayes Theorem

Use-case

The Base theorem gives an interface to revise pr-existing theories or hypothesis (Prior) with given new evidence.

$$\text{ posterior }=\frac{\text{ likelihood }\times \text{ prior }}{\text{ evidence }}\text{. }$$ $$\boxed{P(H\mid E)=\frac{P(E\mid H)P(H)}{P(E)}}$$

Where,

• $P(H|E)$, Posterior Probability is the probability of Hypothesis $H$ given that the evidence $E$ has occurred. (Note: $H$ is one event in the sample space.)
• $P(E|H)$, Likelihood is the Probability of the evidence occurring give that the Hypothesis $H$ is true.
• $P(E|H),$ Prior is the Probability of a Hypothesis that we assume or know before any data is taken into consideration.
• $P(E)$, Evidence is the Probability of the evidence regardless of the Hypothesis.

Note: The Posterior Probability is a calculated value based on new evidence.

In Pattern recognition, the Hypothesis would be the Class and the Evidence would be the features used to make the classification.