مقایسهٔ روش‌ها

	آزمون فاکتور بیز	رگرسیون بیزی	آزمون تی نمونه‌های مستقل	زنجیره مارکوف مونت کارلو (MCMC)
حوزه	بیزی	بیزی	آمار	بیزی
خانواده	Bayesian methods	Bayesian methods	Hypothesis test	Bayesian methods
سال پیدایش	1961	—	1908	—
پدیدآور	Harold Jeffreys	—	Student (W. S. Gosset)	—
نوع	Bayesian hypothesis comparison	Bayesian linear model	Parametric mean comparison	Posterior sampling algorithm
منبع بنیادین	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	Student (1908). The probable error of a mean. Biometrika, 6(1), 1–25.	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
نام‌های دیگر	bayes factor, BF10, Bayesian hypothesis test, Bayes Faktörü — Hipotez Testi	bayesian linear regression, probabilistic regression, bayesian regresyon	student t-test, two-sample t-test, unpaired t-test, bağımsız örneklem t-testi	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)
مرتبط	3	2	4	3
خلاصه	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.	The independent samples t-test is a parametric hypothesis test that compares the means of two independent groups to decide whether they differ significantly. It builds on the t-distribution introduced by Student (W. S. Gosset) in 1908 and assumes the measured values are continuous, approximately normally distributed, and have equal variances.	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.