方法对比

	贝叶斯线性回归	Bayesian Regression	马尔可夫链蒙特卡洛 (MCMC)	普通最小二乘法 (OLS) 回归
领域	贝叶斯	贝叶斯	贝叶斯	计量经济学
方法族	Bayesian methods	Bayesian methods	Bayesian methods	Regression model
起源年份	2013 (modern reference); foundations 18th–19th century	—	—	2019
提出者	Thomas Bayes / Pierre-Simon Laplace (foundations); modern workflow codified by Gelman et al.	—	—	Wooldridge (textbook treatment); classical least squares
类型	Bayesian linear model	Bayesian linear model	Posterior sampling algorithm	Linear regression
开创性文献	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	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
别名	bayesian linear model, probabilistic linear regression, Bayesçi Doğrusal Regresyon	bayesian linear regression, probabilistic regression, bayesian regresyon	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu
相关	4	2	3	5
摘要	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.	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.	Markov Chain Monte Carlo (MCMC) is a family of computational algorithms for sampling from complex probability distributions, most commonly the posterior distributions that arise in Bayesian inference. Rather than computing posteriors analytically — which is rarely possible for realistic models — MCMC constructs a Markov chain whose stationary distribution is the target posterior and draws dependent samples from it, enabling full probabilistic inference for virtually any model.	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).