مقایسهٔ روش‌ها

	رگرسیون بیزی	فرایند گوسی	زنجیره مارکوف مونت کارلو (MCMC)
حوزه	بیزی	یادگیری ماشین	بیزی
خانواده	Bayesian methods	Machine learning	Bayesian methods
سال پیدایش	—	2006 (book); roots in Kriging, 1951)	—
پدیدآور	—	Rasmussen, C. E. & Williams, C. K. I.	—
نوع	Bayesian linear model	Probabilistic non-parametric model	Posterior sampling algorithm
منبع بنیادین	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	Rasmussen, C. E., & Williams, C. K. I. (2006). Gaussian Processes for Machine Learning. MIT Press. ISBN: 978-0-262-18253-9	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	bayesian linear regression, probabilistic regression, bayesian regresyon	GP, Gaussian Process Regression, GPR, Kriging	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)
مرتبط	2	3	3
خلاصه	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.	A Gaussian Process (GP) is a non-parametric, fully probabilistic machine learning model that places a prior distribution directly over functions. Rather than predicting a single value, it returns a predictive mean and a calibrated uncertainty estimate at every test point, making it especially valuable for regression on small to medium datasets and for Bayesian optimization tasks.	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.