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	ベイズ線形回帰	最尤推定法
分野	ベイズ	統計学
系統	Bayesian methods	Regression model
提唱年	2013 (modern reference); foundations 18th–19th century	1922
提唱者	Thomas Bayes / Pierre-Simon Laplace (foundations); modern workflow codified by Gelman et al.	R. A. Fisher
種類	Bayesian linear model	Parametric point estimator
原典	Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955	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	bayesian linear model, probabilistic linear regression, Bayesçi Doğrusal Regresyon	MLE, maximum-likelihood estimator, ML estimation, Fisher's method of maximum likelihood
関連	4	4
概要	Bayesian linear regression is a probabilistic extension of the ordinary linear model, introduced through Bayes' rule and formalised in its modern computational workflow by Gelman et al. (2013). Rather than returning a single point estimate for each coefficient, it combines a user-specified prior distribution with the likelihood of the observed data to produce a full posterior distribution over all parameters, from which credible intervals and posterior predictive distributions are derived.	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.