方法对比

	贝叶斯方差分析 (Bayesian ANOVA)	贝叶斯因子检验	马尔可夫链蒙特卡洛 (MCMC)	单因素方差分析
领域	贝叶斯	贝叶斯	贝叶斯	统计学
方法族	Bayesian methods	Bayesian methods	Bayesian methods	Hypothesis test
起源年份	2012	1961	—	1925
提出者	Rouder, Morey, Speckman & Province	Harold Jeffreys	—	Ronald A. Fisher
类型	Bayesian hypothesis test / group comparison	Bayesian hypothesis comparison	Posterior sampling algorithm	Parametric mean comparison
开创性文献	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.	Jeffreys, H. (1961). Theory of Probability (3rd ed.). Clarendon Press / Oxford University Press. ISBN: 978-0198503682	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	Fisher, R. A. (1925). Statistical Methods for Research Workers. Edinburgh: Oliver and Boyd.
别名	bayesian analysis of variance, bayes factor ANOVA, JZS ANOVA, Bayesçi ANOVA — Bayes Faktörü ile Grup Karşılaştırması	bayes factor, BF10, Bayesian hypothesis test, Bayes Faktörü — Hipotez Testi	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)	one-factor ANOVA, single-factor ANOVA, analysis of variance, tek yönlü ANOVA
相关	4	3	3	4
摘要	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.	The Bayes factor test, formalised by Harold Jeffreys in 1961, is a Bayesian method for comparing two competing hypotheses. Rather than returning a binary reject/retain verdict, it produces a continuous ratio BF₁₀ that quantifies how much more (or less) probable the data are under the alternative hypothesis H₁ than under the null hypothesis H₀.	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.	One-way ANOVA is a parametric hypothesis test that compares the means of three or more independent groups on a single continuous outcome to decide whether at least one group mean differs. It rests on the variance-partitioning framework introduced by Ronald A. Fisher in 1925.