方法对比

	贝叶斯因子检验	Bayesian Regression	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	1961	—	—	1925
提出者	Harold Jeffreys	—	—	Ronald A. Fisher
类型	Bayesian hypothesis comparison	Bayesian linear model	Posterior sampling algorithm	Parametric mean comparison
开创性文献	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	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	bayes factor, BF10, Bayesian hypothesis test, Bayes Faktörü — Hipotez Testi	bayesian linear regression, probabilistic regression, bayesian regresyon	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	3	2	3	4
摘要	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.	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.	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.