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	बहुस्तरीय सन्निकट बायेसियन संगणना	मार्कोव चेन मोंटे कार्लो (MCMC)
क्षेत्र	बायेसियन	अनुकरण
परिवार	Bayesian methods	Process / pipeline
उद्भव वर्ष	2000s–2010s	1953 (Metropolis-Hastings); 1984 (Gibbs)
प्रवर्तक	Extension of ABC (Beaumont et al., 2002) to multilevel/hierarchical settings; developed across multiple authors in the 2010s	Metropolis et al. (1953); Gibbs sampler formalised by Geman & Geman (1984)
प्रकार	Simulation-based Bayesian inference	Simulation-based Bayesian inference / numerical integration
मौलिक स्रोत	Beaumont, M. A., Zhang, W., & Balding, D. J. (2002). Approximate Bayesian computation in population genetics. Genetics, 162(4), 2025–2035.	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.
उपनाम	multilevel ABC, hierarchical ABC, multi-level ABC, ABC for hierarchical models	MCMC, Metropolis-Hastings, Gibbs sampling, Markov Zinciri Monte Carlo (MCMC — Metropolis-Hastings, Gibbs)
संबंधित	6	5
सारांश	Multilevel Approximate Bayesian Computation (multilevel ABC) extends simulation-based Bayesian inference to hierarchically structured data. When the likelihood is intractable and observations are nested within groups, it replaces direct likelihood evaluation with simulations at each level of the hierarchy, accepting parameter draws whose simulated summary statistics are close to the observed ones.	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.