เปรียบเทียบวิธี

	การถดถอยแบบเบย์ (Bayesian Regression)	Hamiltonian Monte Carlo	Markov Chain Monte Carlo (MCMC)
สาขาวิชา	เบย์	เบย์	เบย์
ตระกูล	Bayesian methods	Bayesian methods	Bayesian methods
ปีกำเนิด	—	1987	—
ผู้ริเริ่ม	—	—	—
ประเภท	Bayesian linear model	Gradient-based Markov chain Monte Carlo sampler	Posterior sampling algorithm
แหล่งต้นตำรับ	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	Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987). Hybrid Monte Carlo. Physics Letters B, 195(2), 216–222.	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
ชื่อเรียกอื่น	bayesian linear regression, probabilistic regression, bayesian regresyon	HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)
ที่เกี่ยวข้อง	2	3	3
สรุป	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.	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.	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.