Vertaile menetelmiä

	Bayesilainen regressio	Gibbs-otanta	Hamiltonin Monte Carlo
Tieteenala	Bayesilainen tilastotiede	Bayesilainen tilastotiede	Bayesilainen tilastotiede
Menetelmäperhe	Bayesian methods	Bayesian methods	Bayesian methods
Syntyvuosi	—	1984	1987
Kehittäjä	—	Stuart Geman & Donald Geman	—
Tyyppi	Bayesian linear model	MCMC sampling algorithm	Gradient-based Markov chain Monte Carlo sampler
Alkuperäislähde	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	Geman, S. & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6(6), 721-741.	Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987). Hybrid Monte Carlo. Physics Letters B, 195(2), 216–222.
Rinnakkaisnimet	bayesian linear regression, probabilistic regression, bayesian regresyon	Gibbs sampler, coordinate-wise MCMC, systematic scan Gibbs, blocked Gibbs sampling	HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler
Liittyvät	2	5	3
Tiivistelmä	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.	Gibbs sampling is a Markov chain Monte Carlo algorithm that approximates a high-dimensional posterior distribution by repeatedly drawing each parameter from its full conditional distribution given all other parameters and the data. Because each draw is exact from a conditional — not a proposal that may be rejected — the sampler is efficient when those conditionals are available in closed form.	Hamiltonian Monte Carlo (HMC) is a gradient-based Markov chain Monte Carlo algorithm that uses the geometry of the log-posterior surface to make large, informed jumps through parameter space instead of the small random steps of classical MCMC. Originally introduced for lattice field theory by Duane, Kennedy, Pendleton, and Roweth (1987) under the name Hybrid Monte Carlo, and brought into mainstream statistics by Radford Neal's authoritative 2011 chapter, HMC is today the default sampler in Stan and PyMC and is widely regarded as the state-of-the-art engine for Bayesian posterior inference in high-dimensional models.