手法を比較

	多重レベルモンテカルロ法	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	2008	1993 (particle filter); 2006 (SMC samplers)
提唱者	Michael B. Giles	Gordon, Salmond & Smith (particle filter); Del Moral, Doucet & Jasra (SMC samplers)
種類	variance-reduction simulation	Sequential Bayesian computation
原典	Giles, M. B. (2008). Multilevel Monte Carlo path simulation. Operations Research, 56(3), 607–617.	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	MLMC, multilevel MC, multi-level Monte Carlo, MLMC simulation	SMC, particle filter, sequential importance resampling, SMC sampler
関連	4	6
概要	Multilevel Monte Carlo (MLMC) is a variance-reduction technique that estimates expectations by combining simulations run at multiple levels of numerical resolution. Coarse, cheap simulations capture most of the signal; fine, expensive simulations correct only the remaining small difference — dramatically reducing total computational cost compared with standard Monte Carlo at the finest level alone.	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.