Порівняння методів

	Метод Монте-Карло на основі Марковських ланцюгів (MCMC)	Апроксимаційні байєсівські обчислення
Галузь	Імітаційне моделювання	Імітаційне моделювання
Родина	Process / pipeline	Process / pipeline
Рік появи	1953 (Metropolis-Hastings); 1984 (Gibbs)	2002
Автор методу	Metropolis et al. (1953); Gibbs sampler formalised by Geman & Geman (1984)	—
Тип	Simulation-based Bayesian inference / numerical integration	Simulation-based Bayesian inference
Основоположне джерело	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.
Інші назви	MCMC, Metropolis-Hastings, Gibbs sampling, Markov Zinciri Monte Carlo (MCMC — Metropolis-Hastings, Gibbs)	ABC, likelihood-free inference, simulation-based inference, Yaklaşık Bayesçi Hesaplama (ABC)
Пов'язані	5	5
Підсумок	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.