Сравнение методов

	Байесовская линейная регрессия	Байесовский дисперсионный анализ	Регрессия методом обыкновенных наименьших квадратов (ОНМК)
Область	Байесовские методы	Байесовские методы	Эконометрика
Семейство	Bayesian methods	Bayesian methods	Regression model
Год появления	2013 (modern reference); foundations 18th–19th century	2012	2019
Автор метода	Thomas Bayes / Pierre-Simon Laplace (foundations); modern workflow codified by Gelman et al.	Rouder, Morey, Speckman & Province	Wooldridge (textbook treatment); classical least squares
Тип	Bayesian linear model	Bayesian hypothesis test / group comparison	Linear regression
Основополагающий источник	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	Rouder, J. N., Morey, R. D., Speckman, P. L. & Province, J. M. (2012). Default Bayes Factors for ANOVA Designs. Journal of Mathematical Psychology, 56(5), 356–374.	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860
Другие названия	bayesian linear model, probabilistic linear regression, Bayesçi Doğrusal Regresyon	bayesian analysis of variance, bayes factor ANOVA, JZS ANOVA, Bayesçi ANOVA — Bayes Faktörü ile Grup Karşılaştırması	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu
Связанные	4	4	5
Сводка	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 ANOVA, formalised by Rouder, Morey, Speckman and Province (2012), tests whether group means differ by quantifying the evidence for the alternative hypothesis relative to the null using the Bayes Factor (BF₁₀). Unlike classical ANOVA, it can also measure evidence in favour of the null hypothesis, making it equally informative when groups do not differ.	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).