Σύγκριση μεθόδων

	Μπεϋζιανή Γραμμική Παλινδρόμηση	Μπεϋζιανή Παλινδρόμηση	Αλυσίδες Markov Monte Carlo (MCMC)
Πεδίο	Μπεϋζιανή Στατιστική	Μπεϋζιανή Στατιστική	Μπεϋζιανή Στατιστική
Οικογένεια	Bayesian methods	Bayesian methods	Bayesian methods
Έτος προέλευσης	2013 (modern reference); foundations 18th–19th century	—	—
Δημιουργός	Thomas Bayes / Pierre-Simon Laplace (foundations); modern workflow codified by Gelman et al.	—	—
Τύπος	Bayesian linear model	Bayesian linear model	Posterior sampling algorithm
Θεμελιώδης πηγή	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	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
Εναλλακτικές ονομασίες	bayesian linear model, probabilistic linear regression, Bayesçi Doğrusal Regresyon	bayesian linear regression, probabilistic regression, bayesian regresyon	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)
Συναφείς	4	2	3
Σύνοψη	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.	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.