Methoden vergelijken

	Slice Sampling	Bayesian Regressie	Gibbs Sampling	Hamiltonian Monte Carlo
Vakgebied	Bayesiaanse statistiek	Bayesiaanse statistiek	Bayesiaanse statistiek	Bayesiaanse statistiek
Familie	Bayesian methods	Bayesian methods	Bayesian methods	Bayesian methods
Jaar van ontstaan	2003	—	1984	1987
Grondlegger	Radford M. Neal	—	Stuart Geman & Donald Geman	—
Type	MCMC sampling algorithm	Bayesian linear model	MCMC sampling algorithm	Gradient-based Markov chain Monte Carlo sampler
Oorspronkelijke bron	Neal, R. M. (2003). Slice sampling (with discussion). Annals of Statistics, 31(3), 705–767.	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	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.
Aliassen	slice sampler, Neal slice sampler, uniform slice sampling, auxiliary variable slice sampler	bayesian linear regression, probabilistic regression, bayesian regresyon	Gibbs sampler, coordinate-wise MCMC, systematic scan Gibbs, blocked Gibbs sampling	HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler
Verwant	4	2	5	3
Samenvatting	Slice sampling is a Markov chain Monte Carlo (MCMC) algorithm introduced by Radford M. Neal in his 2003 Annals of Statistics paper. It generates samples from a target distribution by drawing uniformly from the region under the density curve — called the 'slice' — without requiring the user to specify a step-size or proposal distribution, making it self-tuning and broadly applicable for Bayesian posterior inference.	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.	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.