手法を比較

	測定誤差を伴うMetropolis-Hastings法	測定誤差を伴うギブスサンプリング
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1953 (base algorithm); 1990s (measurement-error application)	1990–1993
提唱者	Metropolis et al. (1953); measurement-error extension developed in the 1990s Bayesian literature	Gelfand & Smith (Gibbs sampler); Richardson & Gilks (measurement error extension)
種類	MCMC sampling algorithm	Bayesian MCMC sampling algorithm
原典	Carroll, R. J., Ruppert, D., Stefanski, L. A., & Crainiceanu, C. M. (2006). Measurement Error in Nonlinear Models: A Modern Perspective (2nd ed.). Chapman and Hall/CRC. ISBN: 978-1584886334	Gelfand, A. E. & Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85(410), 398–409.
別名	MH with measurement error, Metropolis-Hastings errors-in-variables, MCMC errors-in-variables, Bayesian errors-in-variables MCMC	Gibbs sampler with errors-in-variables, MCMC measurement error model, Bayesian errors-in-variables Gibbs, Gibbs EIV sampling
関連	4	5
概要	Metropolis-Hastings with measurement error is a Bayesian MCMC approach that jointly estimates model parameters and the true (unobserved) covariate values when predictors or outcomes are recorded with noise. By treating the latent true values as unknown parameters, it propagates measurement uncertainty fully into posterior inference rather than ignoring it or correcting for it post hoc.	Gibbs sampling with measurement error is a Bayesian MCMC method that jointly estimates unknown true covariate values and model parameters when the observed data are corrupted by measurement error. By treating the latent true values as additional unknowns, it samples all quantities iteratively from their full conditional distributions, propagating measurement uncertainty into every downstream inference.