مقایسهٔ روش‌ها

	رگرسیون بیزی	هامیلتونی مونت کارلو	استنتاج بیزی سلسله‌مراتبی
حوزه	بیزی	بیزی	بیزی
خانواده	Bayesian methods	Bayesian methods	Bayesian methods
سال پیدایش	—	1987	1972 (Lindley & Smith); consolidated 1995–2013
پدیدآور	—	—	Lindley & Smith; Gelman et al.
نوع	Bayesian linear model	Gradient-based Markov chain Monte Carlo sampler	Bayesian multilevel model
منبع بنیادین	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
نام‌های دیگر	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
مرتبط	2	3	6
خلاصه	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.