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	ベイズ推論	最尤推定法
分野	統計学	統計学
系統	Bayesian methods	Regression model
提唱年	1763	1922
提唱者	Thomas Bayes; Pierre-Simon Laplace	R. A. Fisher
種類	Probabilistic inference paradigm	Parametric point estimator
原典	Bayes, T. (1763). An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London, 53, 370–418.	Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society of London, Series A, 222, 309–368.
別名	Bayes inference, Bayesian statistics, Bayesian updating, posterior inference	MLE, maximum-likelihood estimator, ML estimation, Fisher's method of maximum likelihood
関連	3	4
概要	Bayesian inference is a statistical paradigm in which probability represents degrees of belief rather than long-run frequencies. It encodes prior knowledge about parameters in a prior distribution, combines that prior with the likelihood of observed data via Bayes' theorem, and produces a posterior distribution that quantifies updated uncertainty. The foundational theorem was published posthumously by Thomas Bayes in 1763 and subsequently systematized by Pierre-Simon Laplace in his 1812 Théorie analytique des probabilités.	Maximum Likelihood Estimation (MLE) is a general-purpose parametric method for estimating the unknown parameters of a statistical model by finding the parameter values that make the observed data most probable. Formalized by R. A. Fisher in his landmark 1922 paper in the Philosophical Transactions of the Royal Society, MLE has become the dominant parameter-estimation paradigm in modern statistics and is the foundational engine behind logistic regression, generalized linear models, structural equation modeling, and virtually all parametric inference procedures.