手法を比較

	モデル比較のためのMCMC	ハミルトニアンモンテカルロ
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1995	1987
提唱者	Peter J. Green (reversible-jump MCMC); Meng & Wong (bridge sampling)	—
種類	Bayesian computational method	Gradient-based Markov chain Monte Carlo sampler
原典	Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82(4), 711–732.	Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987). Hybrid Monte Carlo. Physics Letters B, 195(2), 216–222.
別名	reversible-jump MCMC, RJMCMC, marginal likelihood estimation via MCMC, Bayesian model selection via MCMC	HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler
関連	5	3
概要	MCMC for model comparison uses Markov chain Monte Carlo algorithms to estimate the marginal likelihoods and Bayes factors needed to formally compare competing statistical models. Techniques such as reversible-jump MCMC and bridge sampling allow exploration across model spaces of different dimensionality, enabling fully Bayesian model selection and averaging.	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.