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	Multilevel Monte Carlo Simulation	Markov Chain Monte Carlo (MCMC)
Ämnesområde	Bayesiansk statistik	Simulering
Familj	Bayesian methods	Process / pipeline
Ursprungsår	2008	1953 (Metropolis-Hastings); 1984 (Gibbs)
Upphovsperson	Michael B. Giles	Metropolis et al. (1953); Gibbs sampler formalised by Geman & Geman (1984)
Typ	variance-reduction simulation	Simulation-based Bayesian inference / numerical integration
Ursprungskälla	Giles, M. B. (2008). Multilevel Monte Carlo path simulation. Operations Research, 56(3), 607–617.	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.
Alias	MLMC, multilevel MC, multi-level Monte Carlo, MLMC simulation	MCMC, Metropolis-Hastings, Gibbs sampling, Markov Zinciri Monte Carlo (MCMC — Metropolis-Hastings, Gibbs)
Närliggande	4	5
Sammanfattning	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.	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.