手法を比較

	メトロポリス・ヘイスティングス法	逐次モンテカルロ法
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1953	1993 (particle filter); 2006 (SMC samplers)
提唱者	Metropolis et al. (1953); generalised by Hastings (1970)	Gordon, Salmond & Smith (particle filter); Del Moral, Doucet & Jasra (SMC samplers)
種類	Markov chain Monte Carlo sampler	Sequential Bayesian computation
原典	Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953). Equation of state calculations by fast computing machines. The Journal of Chemical Physics, 21(6), 1087–1092.	Gordon, N. J., Salmond, D. J., & Smith, A. F. M. (1993). Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proceedings F - Radar and Signal Processing, 140(2), 107–113.
別名	MH algorithm, M-H algorithm, Metropolis algorithm, Metropolis-Hastings sampler	SMC, particle filter, sequential importance resampling, SMC sampler
関連	5	6
概要	The Metropolis-Hastings (MH) algorithm is a general-purpose Markov chain Monte Carlo (MCMC) method for drawing samples from any probability distribution whose density can be evaluated up to a normalising constant. Introduced by Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller (1953) in computational physics and generalised by Hastings (1970) to asymmetric proposal distributions, it is the foundational algorithm from which nearly all subsequent MCMC samplers — Gibbs sampling, Hamiltonian Monte Carlo, slice sampling — are derived or can be viewed as special cases.	Sequential Monte Carlo (SMC) is a family of simulation-based algorithms that approximate evolving probability distributions by propagating and reweighting a cloud of weighted random draws called particles. It handles nonlinear, non-Gaussian models and streams of data naturally, making it the method of choice for real-time state estimation and posterior approximation over complex distributions.