مقایسهٔ روش‌ها

	رگرسیون خطی بیزی	رگرسیون بیزی	رگرسیون حداقل مربعات معمولی (OLS)
حوزه	بیزی	بیزی	اقتصادسنجی
خانواده	Bayesian methods	Bayesian methods	Regression model
سال پیدایش	2013 (modern reference); foundations 18th–19th century	—	2019
پدیدآور	Thomas Bayes / Pierre-Simon Laplace (foundations); modern workflow codified by Gelman et al.	—	Wooldridge (textbook treatment); classical least squares
نوع	Bayesian linear model	Bayesian linear model	Linear regression
منبع بنیادین	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
نام‌های دیگر	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
مرتبط	4	2	5
خلاصه	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).