Methoden vergleichen

	Bayes'sche Lineare Regression	Bayes'sche Regression	Methode der kleinsten Quadrate (OLS)
Fachgebiet	Bayes-Statistik	Bayes-Statistik	Ökonometrie
Familie	Bayesian methods	Bayesian methods	Regression model
Entstehungsjahr	2013 (modern reference); foundations 18th–19th century	—	2019
Urheber	Thomas Bayes / Pierre-Simon Laplace (foundations); modern workflow codified by Gelman et al.	—	Wooldridge (textbook treatment); classical least squares
Typ	Bayesian linear model	Bayesian linear model	Linear regression
Wegweisende Quelle	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	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	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860
Aliasnamen	bayesian linear model, probabilistic linear regression, Bayesçi Doğrusal Regresyon	bayesian linear regression, probabilistic regression, bayesian regresyon	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu
Verwandt	4	2	5
Zusammenfassung	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.	Bayesian regression is a probabilistic version of linear regression that treats the model parameters as uncertain quantities. Instead of returning a single best-fit estimate, it combines prior knowledge with the observed data to produce a full posterior probability distribution for each parameter, from which credible intervals and predictions are read off.	Ordinary Least Squares is the classical linear regression method that explains a continuous outcome as a linear combination of predictors. It estimates the coefficients by minimising the sum of squared residuals, and under the Gauss-Markov assumptions these estimates are the best linear unbiased estimator (BLUE).