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Bayesian probability is one interpretation of the concept of probability. In contrast to interpreting probability as frequency or propensity of some phenomenon, Bayesian probability is a quantity that we assign to represent a state of knowledge,〔Jaynes, E.T. "Bayesian Methods: General Background." In Maximum-Entropy and Bayesian Methods in Applied Statistics, by J. H. Justice (ed.). Cambridge: Cambridge Univ. Press, 1986〕 or a state of belief.〔 In the Bayesian view, a probability is assigned to a hypothesis, whereas under frequentist inference, a hypothesis is typically tested without being assigned a probability. The Bayesian interpretation of probability can be seen as an extension of propositional logic that enables reasoning with hypotheses, i.e., the propositions whose truth or falsity is uncertain. Bayesian probability belongs to the category of evidential probabilities; 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 (evidence).〔Paulos, John Allen. (''The Mathematics of Changing Your Mind,'' ) New York Times (US). August 5, 2011; retrieved 2011-08-06〕 The Bayesian interpretation provides a standard set of procedures and formulae to perform this calculation. The term "Bayesian" derives from the 18th century mathematician and theologian Thomas Bayes, who provided the first mathematical treatment of a non-trivial problem of Bayesian inference.〔Stigler, Stephen M. (1986) ''The history of statistics.'' Harvard University Press. pg 131.〕 Mathematician Pierre-Simon Laplace pioneered and popularised what is now called Bayesian probability.〔Stigler, Stephen M. (1986) ''The history of statistics.'', Harvard University press. pp. 97–98, 131.〕 Broadly speaking, there are two views on Bayesian probability that interpret the ''probability'' 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.〔〔Cox, Richard T. ''Algebra of Probable Inference'', The Johns Hopkins University Press, 2001〕 According to the ''subjectivist view'', probability quantifies a "personal belief".〔de Finetti, B. (1974) ''Theory of probability'' (2 vols.), J. Wiley & Sons, Inc., New York〕 ==Bayesian methodology== Bayesian methods are characterized by the following concepts and procedures: * The use of random variables, or, more generally, unknown quantities,〔 to model all sources of uncertainty in statistical models. This also includes uncertainty resulting from lack of information (see also the aleatoric and epistemic uncertainty). * The need to determine the ''prior probability distribution'' taking into account the available (prior) information. * The ''sequential use of the Bayes' formula'': when more data becomes available, calculate the ''posterior distribution'' using the Bayes' formula; subsequently, the posterior distribution becomes the next prior. * For the frequentist a hypothesis is a proposition (which must be either true or false), so that the frequentist probability of a hypothesis is either one or zero. In Bayesian statistics, a probability can be assigned to a hypothesis that can differ from 0 or 1 if the truth value is uncertain. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Bayesian probability」の詳細全文を読む スポンサード リンク
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