# Bayesian inference

## Method of statistical inference / From Wikipedia, the free encyclopedia

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**Bayesian inference** (/ˈbeɪziən/ *BAY-zee-ən* or /ˈbeɪʒən/ *BAY-zhən*)^{[1]} is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Fundamentally, Bayesian inference uses prior knowledge, in the form of a prior distribution in order to estimate posterior probabilities. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law. In the philosophy of decision theory, Bayesian inference is closely related to subjective probability, often called "Bayesian probability".