手法を比較

	モデル比較のためのメトロポリス・ヘイスティングス法	モデル比較のためのMCMC
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1970 (extended 1995)	1995
提唱者	W. K. Hastings (1970); extended for model comparison by P. J. Green (1995)	Peter J. Green (reversible-jump MCMC); Meng & Wong (bridge sampling)
種類	MCMC-based model comparison	Bayesian computational method
原典	Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1), 97-109.	Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82(4), 711–732.
別名	MH model comparison, Metropolis-Hastings Bayes factor estimation, reversible-jump Metropolis-Hastings, MH model selection	reversible-jump MCMC, RJMCMC, marginal likelihood estimation via MCMC, Bayesian model selection via MCMC
関連	4	5
概要	Metropolis-Hastings for model comparison uses the Metropolis-Hastings MCMC algorithm to explore both parameter and model space simultaneously, producing posterior probabilities for competing models and enabling Bayes factor estimation without requiring closed-form marginal likelihoods. The canonical extension — reversible-jump MCMC by Green (1995) — handles models of different dimensionalities within a single sampler.	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.