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	Gibbs sampling	Hamiltonian Monte Carlo	Hierarkisk Bayesiansk inferens
Ämnesområde	Bayesiansk statistik	Bayesiansk statistik	Bayesiansk statistik
Familj	Bayesian methods	Bayesian methods	Bayesian methods
Ursprungsår	1984	1987	1972 (Lindley & Smith); consolidated 1995–2013
Upphovsperson	Stuart Geman & Donald Geman	—	Lindley & Smith; Gelman et al.
Typ	MCMC sampling algorithm	Gradient-based Markov chain Monte Carlo sampler	Bayesian multilevel model
Ursprungskälla	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.	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	Gibbs sampler, coordinate-wise MCMC, systematic scan Gibbs, blocked Gibbs sampling	HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler	multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model
Närliggande	5	3	6
Sammanfattning	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.	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.