Bayes Theorem

probability-theory bayesian-statistics

Definition

Bayes Theorem

Rewriting the definition of the conditional probability for and gives the multiplication theorems:

which leads to Bayes Theorem:

The Bayes Theorem describes the probability of an event based on prior knowledge (before observation) and allows to update the prior knowledge after observation to the posterior (after observation).

Law of Total Probability

Updating Beliefs

Combing the law of total probability gives a partition of with Bayes Theorem, we get the alternative form:

where the events are often referred to as Hypothesis. We call the prior probability and the posterior probability.