Vertaile menetelmiä

	Markov Chain Monte Carlo (MCMC)	Bayesilainen regressio
Tieteenala	Simulointi	Bayesilainen tilastotiede
Menetelmäperhe	Process / pipeline	Bayesian methods
Syntyvuosi	1953 (Metropolis-Hastings); 1984 (Gibbs)	—
Kehittäjä	Metropolis et al. (1953); Gibbs sampler formalised by Geman & Geman (1984)	—
Tyyppi	Simulation-based Bayesian inference / numerical integration	Bayesian linear model
Alkuperäislähde	Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A. & Rubin, D.B. (2013). Bayesian Data Analysis (3rd ed.). Chapman & Hall/CRC.	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	MCMC, Metropolis-Hastings, Gibbs sampling, Markov Zinciri Monte Carlo (MCMC — Metropolis-Hastings, Gibbs)	bayesian linear regression, probabilistic regression, bayesian regresyon
Liittyvät	5	2
Tiivistelmä	Markov Chain Monte Carlo (MCMC) is a family of simulation algorithms that constructs a Markov chain whose stationary distribution is the target posterior, enabling Bayesian inference and high-dimensional integral computation that would otherwise be analytically intractable. Pioneered by Metropolis and colleagues in 1953 and extended by Hastings in 1970, MCMC underpins modern Bayesian statistics. The two most widely used variants are Metropolis-Hastings, which proposes moves from a general proposal distribution, and Gibbs sampling, which draws each parameter in turn from its full conditional distribution.	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.