手法を比較

	スライスサンプリング	ハミルトニアンモンテカルロ	マルコフ連鎖モンテカルロ法 (MCMC)
分野	ベイズ	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods	Bayesian methods
提唱年	2003	1987	—
提唱者	Radford M. Neal	—	—
種類	MCMC sampling algorithm	Gradient-based Markov chain Monte Carlo sampler	Posterior sampling algorithm
原典	Neal, R. M. (2003). Slice sampling (with discussion). Annals of Statistics, 31(3), 705–767.	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
別名	slice sampler, Neal slice sampler, uniform slice sampling, auxiliary variable slice sampler	HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)
関連	4	3	3
概要	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.	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.	Markov Chain Monte Carlo (MCMC) is a family of computational algorithms for sampling from complex probability distributions, most commonly the posterior distributions that arise in Bayesian inference. Rather than computing posteriors analytically — which is rarely possible for realistic models — MCMC constructs a Markov chain whose stationary distribution is the target posterior and draws dependent samples from it, enabling full probabilistic inference for virtually any model.