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	बायेसियन अनुमान	बायेसियन रैखिक प्रतिगमन (Bayesian Linear Regression)	स्वतंत्र प्रतिदर्श t-परीक्षण
क्षेत्र	सांख्यिकी	बायेसियन	सांख्यिकी
परिवार	Bayesian methods	Bayesian methods	Hypothesis test
उद्भव वर्ष	1763	2013 (modern reference); foundations 18th–19th century	1908
प्रवर्तक	Thomas Bayes; Pierre-Simon Laplace	Thomas Bayes / Pierre-Simon Laplace (foundations); modern workflow codified by Gelman et al.	Student (W. S. Gosset)
प्रकार	Probabilistic inference paradigm	Bayesian linear model	Parametric mean comparison
मौलिक स्रोत	Bayes, T. (1763). An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London, 53, 370–418.	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.
उपनाम	Bayes inference, Bayesian statistics, Bayesian updating, posterior inference	bayesian linear model, probabilistic linear regression, Bayesçi Doğrusal Regresyon	student t-test, two-sample t-test, unpaired t-test, bağımsız örneklem t-testi
संबंधित	3	4	4
सारांश	Bayesian inference is a statistical paradigm in which probability represents degrees of belief rather than long-run frequencies. It encodes prior knowledge about parameters in a prior distribution, combines that prior with the likelihood of observed data via Bayes' theorem, and produces a posterior distribution that quantifies updated uncertainty. The foundational theorem was published posthumously by Thomas Bayes in 1763 and subsequently systematized by Pierre-Simon Laplace in his 1812 Théorie analytique des probabilités.	Bayesian linear regression is a probabilistic extension of the ordinary linear model, introduced through Bayes' rule and formalised in its modern computational workflow by Gelman et al. (2013). Rather than returning a single point estimate for each coefficient, it combines a user-specified prior distribution with the likelihood of the observed data to produce a full posterior distribution over all parameters, from which credible intervals and posterior predictive distributions are derived.	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.