Sammenlign metoder

	Gibbs Sampling	Hamiltonian Monte Carlo
Fagområde	Bayesiansk	Bayesiansk
Familie	Bayesian methods	Bayesian methods
Oprindelsesår	1984	1987
Ophavsperson	Stuart Geman & Donald Geman	—
Type	MCMC sampling algorithm	Gradient-based Markov chain Monte Carlo sampler
Oprindelig kilde	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.
Aliasser	Gibbs sampler, coordinate-wise MCMC, systematic scan Gibbs, blocked Gibbs sampling	HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler
Relaterede	5	3
Resumé	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.