手法を比較

	逐次モンテカルロ法	ハミルトニアンモンテカルロ
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1993 (particle filter); 2006 (SMC samplers)	1987
提唱者	Gordon, Salmond & Smith (particle filter); Del Moral, Doucet & Jasra (SMC samplers)	—
種類	Sequential Bayesian computation	Gradient-based Markov chain Monte Carlo sampler
原典	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.	Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987). Hybrid Monte Carlo. Physics Letters B, 195(2), 216–222.
別名	SMC, particle filter, sequential importance resampling, SMC sampler	HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler
関連	6	3
概要	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.	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.