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	Bayesiansk linjär regression	Maximum Likelihood Estimation
Ämnesområde	Bayesiansk statistik	Statistik
Familj	Bayesian methods	Regression model
Ursprungsår	2013 (modern reference); foundations 18th–19th century	1922
Upphovsperson	Thomas Bayes / Pierre-Simon Laplace (foundations); modern workflow codified by Gelman et al.	R. A. Fisher
Typ	Bayesian linear model	Parametric point estimator
Ursprungskälla	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.
Alias	bayesian linear model, probabilistic linear regression, Bayesçi Doğrusal Regresyon	MLE, maximum-likelihood estimator, ML estimation, Fisher's method of maximum likelihood
Närliggande	4	4
Sammanfattning	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.