قارن الطرق

	محاكاة مونت كارلو متعددة المستويات	سلسلة ماركوف مونت كارلو (MCMC)
المجال	بايزي	المحاكاة
العائلة	Bayesian methods	Process / pipeline
سنة النشأة	2008	1953 (Metropolis-Hastings); 1984 (Gibbs)
صاحب الطريقة	Michael B. Giles	Metropolis et al. (1953); Gibbs sampler formalised by Geman & Geman (1984)
النوع	variance-reduction simulation	Simulation-based Bayesian inference / numerical integration
المصدر التأسيسي	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.
الأسماء البديلة	MLMC, multilevel MC, multi-level Monte Carlo, MLMC simulation	MCMC, Metropolis-Hastings, Gibbs sampling, Markov Zinciri Monte Carlo (MCMC — Metropolis-Hastings, Gibbs)
ذات صلة	4	5
الملخص	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.