手法を比較

	モンテカルロシミュレーションのための分散削減技術	マルコフ連鎖モンテカルロ法（MCMC）
分野	シミュレーション	シミュレーション
系統	Process / pipeline	Process / pipeline
提唱年	1950s–1980s (technique family)	1953 (Metropolis-Hastings); 1984 (Gibbs)
提唱者	Hammersley & Morton (antithetic variates, 1956); Lavenberg & Welch (control variates, 1981); importance sampling roots in Kahn & Marshall (1953)	Metropolis et al. (1953); Gibbs sampler formalised by Geman & Geman (1984)
種類	Simulation variance-reduction technique family	Simulation-based Bayesian inference / numerical integration
原典	Ross, S.M. (2012). Simulation (5th ed.). Academic Press. ISBN: 978-0124158252	Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A. & Rubin, D.B. (2013). Bayesian Data Analysis (3rd ed.). Chapman & Hall/CRC.
別名	antithetic variates, control variates, importance sampling, stratified sampling MC	MCMC, Metropolis-Hastings, Gibbs sampling, Markov Zinciri Monte Carlo (MCMC — Metropolis-Hastings, Gibbs)
関連	4	5
概要	Variance reduction techniques are a family of methods that improve the efficiency of Monte Carlo simulation by achieving the same estimation accuracy with fewer random draws. Developed incrementally from the 1950s onward — with antithetic variates attributed to Hammersley and Morton, control variates formalised by Lavenberg and Welch, and importance sampling rooted in Kahn and Marshall — the family includes antithetic variates (AV), control variates (CV), importance sampling (IS), and stratification, each exploiting a different structural property of the target quantity to lower estimator variance without introducing bias.	Markov Chain Monte Carlo (MCMC) is a family of simulation algorithms that constructs a Markov chain whose stationary distribution is the target posterior, enabling Bayesian inference and high-dimensional integral computation that would otherwise be analytically intractable. Pioneered by Metropolis and colleagues in 1953 and extended by Hastings in 1970, MCMC underpins modern Bayesian statistics. The two most widely used variants are Metropolis-Hastings, which proposes moves from a general proposal distribution, and Gibbs sampling, which draws each parameter in turn from its full conditional distribution.