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	Multilevel MCMC	Hamiltonian Monte Carlo
Ämnesområde	Bayesiansk statistik	Bayesiansk statistik
Familj	Bayesian methods	Bayesian methods
Ursprungsår	1990s	1987
Upphovsperson	Gelfand & Smith (sampling-based approach); multilevel extension developed through 1990s Bayesian hierarchical modeling literature	—
Typ	Bayesian computational inference	Gradient-based Markov chain Monte Carlo sampler
Ursprungskälla	Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955	Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987). Hybrid Monte Carlo. Physics Letters B, 195(2), 216–222.
Alias	hierarchical MCMC, multilevel Bayesian sampling, MLMCMC, hierarchical Markov chain Monte Carlo	HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler
Närliggande	6	3
Sammanfattning	Multilevel MCMC applies Markov chain Monte Carlo sampling to hierarchical (multilevel) Bayesian models. It draws samples from the joint posterior of both group-level and population-level parameters simultaneously, propagating uncertainty across levels and enabling inference in clustered or nested data structures where observations within groups share common distributional characteristics.	Hamiltonian Monte Carlo (HMC) is a gradient-based Markov chain Monte Carlo algorithm that uses the geometry of the log-posterior surface to make large, informed jumps through parameter space instead of the small random steps of classical MCMC. Originally introduced for lattice field theory by Duane, Kennedy, Pendleton, and Roweth (1987) under the name Hybrid Monte Carlo, and brought into mainstream statistics by Radford Neal's authoritative 2011 chapter, HMC is today the default sampler in Stan and PyMC and is widely regarded as the state-of-the-art engine for Bayesian posterior inference in high-dimensional models.