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	ベイズ因子検定	ベイズ回帰	マルコフ連鎖モンテカルロ法 (MCMC)	一元配置分散分析
分野	ベイズ	ベイズ	ベイズ	統計学
系統	Bayesian methods	Bayesian methods	Bayesian methods	Hypothesis test
提唱年	1961	—	—	1925
提唱者	Harold Jeffreys	—	—	Ronald A. Fisher
種類	Bayesian hypothesis comparison	Bayesian linear model	Posterior sampling algorithm	Parametric mean comparison
原典	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.
別名	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
関連	3	2	3	4
概要	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.