مقایسهٔ روش‌ها

	زنجیره مارکوف مونت کارلو (MCMC)	محاسبات بیزی تقریبی
حوزه	شبیه‌سازی	شبیه‌سازی
خانواده	Process / pipeline	Process / pipeline
سال پیدایش	1953 (Metropolis-Hastings); 1984 (Gibbs)	2002
پدیدآور	Metropolis et al. (1953); Gibbs sampler formalised by Geman & Geman (1984)	—
نوع	Simulation-based Bayesian inference / numerical integration	Simulation-based Bayesian inference
منبع بنیادین	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.	Beaumont, M.A., Zhang, W. & Balding, D.J. (2002). Approximate Bayesian Computation in Population Genetics. Genetics, 162(4), 2025-2035.
نام‌های دیگر	MCMC, Metropolis-Hastings, Gibbs sampling, Markov Zinciri Monte Carlo (MCMC — Metropolis-Hastings, Gibbs)	ABC, likelihood-free inference, simulation-based inference, Yaklaşık Bayesçi Hesaplama (ABC)
مرتبط	5	5
خلاصه	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.	Approximate Bayesian Computation (ABC) is a family of simulation-based inference methods that estimate posterior distributions without requiring an analytically tractable likelihood function. Introduced by Beaumont, Zhang and Balding (2002) in the context of population genetics, ABC replaced the intractable likelihood with repeated model simulation and a comparison of summary statistics between simulated and observed data.