Editing Bayesian inference (section)

{{Short description|Method of statistical inference}}
{{Bayesian statistics}}
'''Bayesian inference''' ({{IPAc-en|ˈ|b|eɪ|z|i|ə|n}} {{respell|BAY|zee|ən}} or {{IPAc-en|ˈ|b|eɪ|ʒ|ən}} {{respell|BAY|zhən}}){{refn|{{MerriamWebsterDictionary|=2023-08-12|Bayesian}}}} is a method of [[statistical inference]] in which [[Bayes' theorem]] is used to calculate a probability of a hypothesis, given prior [[evidence]], and update it as more [[information]] becomes available. Fundamentally, Bayesian inference uses a [[Prior probability|prior distribution]] to estimate [[Posterior probability|posterior probabilities.]] Bayesian inference is an important technique in [[statistics]], and especially in [[mathematical statistics]]. Bayesian updating is particularly important in the [[Sequential analysis|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]]".
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; however, non-Bayesian updating rules are compatible with rationality, according to philosophers [[Ian Hacking]] and [[Bas van&nbsp;Fraassen]].<ref>Stanford encyclopedia of philosophy; Bayesian Epistemology; http://plato.stanford.edu/entries/epistemology-bayesian</ref><ref>Gillies, Donald (2000); "Philosophical Theories of Probability"; Routledge; Chapter 4 "The subjective theory"</ref>
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