Methoden vergleichen

	Bayes'sche ANOVA	Markov-Kette Monte Carlo (MCMC)	Methode der kleinsten Quadrate (OLS)
Fachgebiet	Bayes-Statistik	Bayes-Statistik	Ökonometrie
Familie	Bayesian methods	Bayesian methods	Regression model
Entstehungsjahr	2012	—	2019
Urheber	Rouder, Morey, Speckman & Province	—	Wooldridge (textbook treatment); classical least squares
Typ	Bayesian hypothesis test / group comparison	Posterior sampling algorithm	Linear regression
Wegweisende Quelle	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.	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 analysis of variance, bayes factor ANOVA, JZS ANOVA, Bayesçi ANOVA — Bayes Faktörü ile Grup Karşılaştırması	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu
Verwandt	4	3	5
Zusammenfassung	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.	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).