Bayesian probability is one of the most popular interpretations of the concept of probability. The Bayesian interpretation of probability can be seen as an extension of logic that enables reasoning with uncertain statements. To evaluate the probability of a hypothesis, the Bayesian probabilist specifies some prior probability, which is then updated in the light of new relevant data.

The Bayesian interpretation provides a standard set of procedures and formulae to perform this calculation. Bayesian probability interprets the concept of probability as "a measure of a state of knowledge", in contrast to interpreting it as a frequency or a physical property of a system. Its name is derived from the 18th century statistician Thomas Bayes, who pioneered some of the concepts.

Broadly speaking, there are two views on Bayesian probability that interpret the state of knowledge concept in different ways. According to the objectivist view, the rules of Bayesian statistics can be justified by requirements of rationality and consistency and interpreted as an extension of logic. According to the subjectivist view, the state of knowledge measures a "personal belief".

Many modern machine learning methods are based on objectivist Bayesian principles. One of the crucial features of the Bayesian view is that a probability is assigned to a hypothesis, whereas under the frequentist view, a hypothesis is typically rejected or not rejected without directly assigning a probability. The probability of a hypothesis given the data (the posterior) is proportional to the product of the likelihood times the prior probability (often just called the prior).

The likelihood brings in the effect of the data, while the prior specifies the belief in the hypothesis before the data was observed.

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