# Bayesian Probability

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**Formula:** `P(A|B) = (P(B|A) * P(A)) / P(B)`

Bayesian probability is a method of probability interpretation that updates the probability estimate for a hypothesis as additional evidence is acquired. This dynamic update process is known as Bayesian inference. The formula for Bayesian probability takes into account a prior probability `P(A)`

, which is the initial estimation of the likelihood of a hypothesis before any new evidence is introduced. The likelihood `P(B|A)`

is the probability of the new evidence given the hypothesis. Finally, the marginal likelihood `P(B)`

is the probability of the new evidence under all possible hypotheses. The updated probability, `P(A|B)`

, is the degree of belief in the hypothesis after considering the new evidence.

Bayesian probability is useful in many practical applications including spam filtering, medical diagnosis, and machine learning algorithms, where it helps to make informed decisions based on evolving data.

Tags: Statistics, Probability, Bayesian Inference