Vertaile menetelmiä

	Metropolis-Hastings-algoritmi	Bayesilainen regressio
Tieteenala	Bayesilainen tilastotiede	Bayesilainen tilastotiede
Menetelmäperhe	Bayesian methods	Bayesian methods
Syntyvuosi	1953	—
Kehittäjä	Metropolis et al. (1953); generalised by Hastings (1970)	—
Tyyppi	Markov chain Monte Carlo sampler	Bayesian linear model
Alkuperäislähde	Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953). Equation of state calculations by fast computing machines. The Journal of Chemical Physics, 21(6), 1087–1092.	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
Rinnakkaisnimet	MH algorithm, M-H algorithm, Metropolis algorithm, Metropolis-Hastings sampler	bayesian linear regression, probabilistic regression, bayesian regresyon
Liittyvät	5	2
Tiivistelmä	The Metropolis-Hastings (MH) algorithm is a general-purpose Markov chain Monte Carlo (MCMC) method for drawing samples from any probability distribution whose density can be evaluated up to a normalising constant. Introduced by Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller (1953) in computational physics and generalised by Hastings (1970) to asymmetric proposal distributions, it is the foundational algorithm from which nearly all subsequent MCMC samplers — Gibbs sampling, Hamiltonian Monte Carlo, slice sampling — are derived or can be viewed as special cases.	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.