手法を比較

	マルコフ連鎖モンテカルロ法 (MCMC)	ベイズモデル平均	ベイズ回帰
分野	ベイズ	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods	Bayesian methods
提唱年	—	1999	—
提唱者	—	Hoeting, Madigan, Raftery & Volinsky	—
種類	Posterior sampling algorithm	Bayesian model averaging	Bayesian linear model
原典	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	Hoeting, J. A., Madigan, D., Raftery, A. E. & Volinsky, C. T. (1999). Bayesian Model Averaging: A Tutorial. Statistical Science, 14(4), 382–401.	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
別名	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)	BMA, Bayesian model combination, Bayesian Model Ortalaması (BMA)	bayesian linear regression, probabilistic regression, bayesian regresyon
関連	3	5	2
概要	Markov Chain Monte Carlo (MCMC) is a family of computational algorithms for sampling from complex probability distributions, most commonly the posterior distributions that arise in Bayesian inference. Rather than computing posteriors analytically — which is rarely possible for realistic models — MCMC constructs a Markov chain whose stationary distribution is the target posterior and draws dependent samples from it, enabling full probabilistic inference for virtually any model.	Bayesian Model Averaging (BMA), formalised as a tutorial by Hoeting, Madigan, Raftery and Volinsky in 1999, addresses model uncertainty by averaging over all plausible model specifications rather than selecting a single best model. Each candidate model receives a posterior probability that reflects how well it fits the data given a prior, and predictions or coefficient estimates are formed as weighted averages across the entire model space. This approach reduces the bias and overconfidence that arise when a single selected model is treated as the true one.	Bayesian regression is a probabilistic version of linear regression that treats the model parameters as uncertain quantities. Instead of returning a single best-fit estimate, it combines prior knowledge with the observed data to produce a full posterior probability distribution for each parameter, from which credible intervals and predictions are read off.