Bandingkan kaedah

	Regresi Bayesian	Hamiltonian Monte Carlo	Inferensi Bayesian Hierarki
Bidang	Bayesian	Bayesian	Bayesian
Keluarga	Bayesian methods	Bayesian methods	Bayesian methods
Tahun asal	—	1987	1972 (Lindley & Smith); consolidated 1995–2013
Pengasas	—	—	Lindley & Smith; Gelman et al.
Jenis	Bayesian linear model	Gradient-based Markov chain Monte Carlo sampler	Bayesian multilevel model
Sumber perintis	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
Alias	bayesian linear regression, probabilistic regression, bayesian regresyon	HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler	multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model
Berkaitan	2	3	6
Ringkasan	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.	Hierarchical Bayesian inference is a probabilistic modeling framework that organises parameters into levels, placing priors on the group-level parameters and hyperpriors on the parameters governing those priors. It enables partial pooling of information across groups, balancing the extremes of treating each group as independent or merging them into a single estimate.