Bayeszis
Bayes's theorem, named after the Reverend Thomas Bayes (1701–1761), is a fundamental principle in probability theory that describes how to update the probability of a hypothesis when given evidence. It provides a mathematical framework for reasoning about uncertain events and is widely used in statistics, machine learning, artificial intelligence, and various scientific disciplines.
The theorem is expressed as a formula that relates the conditional and marginal probabilities of random events.
P(H|E) = [P(E|H) * P(H)] / P(E)
Here, P(H|E) is the posterior probability, P(E|H) is the likelihood, P(H) is the prior probability, and P(E)
Bayes's theorem is particularly useful in situations where prior knowledge about a hypothesis can be incorporated
Despite its utility, Bayes's theorem requires careful handling of prior probabilities, which can sometimes introduce bias