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| Slice Sampling× | Bayes'sche Regression× | Hamiltonian Monte Carlo× | |
|---|---|---|---|
| Fachgebiet | Bayes-Statistik | Bayes-Statistik | Bayes-Statistik |
| Familie | Bayesian methods | Bayesian methods | Bayesian methods |
| Entstehungsjahr≠ | 2003 | — | 1987 |
| Urheber≠ | Radford M. Neal | — | — |
| Typ≠ | MCMC sampling algorithm | Bayesian linear model | Gradient-based Markov chain Monte Carlo sampler |
| Wegweisende Quelle≠ | Neal, R. M. (2003). Slice sampling (with discussion). Annals of Statistics, 31(3), 705–767. DOI ↗ | 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. DOI ↗ |
| Aliasnamen≠ | slice sampler, Neal slice sampler, uniform slice sampling, auxiliary variable slice sampler | bayesian linear regression, probabilistic regression, bayesian regresyon | HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler |
| Verwandt≠ | 4 | 2 | 3 |
| Zusammenfassung≠ | 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. | 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. |
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