مقایسهٔ روش‌ها

	شبیه‌سازی مونت کارلو بیزی	زنجیره مارکوف مونت کارلو (MCMC)
حوزه	شبیه‌سازی	شبیه‌سازی
خانواده	Process / pipeline	Process / pipeline
سال پیدایش	1987–1990s	1953 (Metropolis-Hastings); 1984 (Gibbs)
پدیدآور	O'Hagan, A. and colleagues	Metropolis et al. (1953); Gibbs sampler formalised by Geman & Geman (1984)
نوع	Simulation / uncertainty quantification	Simulation-based Bayesian inference / numerical integration
منبع بنیادین	O'Hagan, A., Buck, C. E., Daneshkhah, A., Eiser, J. R., Garthwaite, P. H., Jenkinson, D. J., Oakley, J. E., & Rakow, T. (2006). Uncertain Judgements: Eliciting Experts' Probabilities. Wiley. ISBN: 9780470029992	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.
نام‌های دیگر	Bayesian MC, BMC simulation, Bayesian stochastic simulation, Bayesian uncertainty propagation	MCMC, Metropolis-Hastings, Gibbs sampling, Markov Zinciri Monte Carlo (MCMC — Metropolis-Hastings, Gibbs)
مرتبط	4	5
خلاصه	Bayesian Monte Carlo Simulation integrates Bayesian statistical inference with Monte Carlo sampling to propagate uncertainty through complex models. Instead of drawing samples from arbitrary distributions, it conditions sampling on observed data and expert prior knowledge via Bayes' theorem, yielding posterior-based uncertainty estimates that are both statistically coherent and interpretable in probabilistic terms.	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.