手法を比較

	測定誤差を伴うハミルトニアン・モンテカルロ法	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	2006-2011	1990–1993
提唱者	Neal (2011) for HMC; Carroll et al. (2006) for measurement error framework	Gelfand & Smith (Gibbs sampler); Richardson & Gilks (measurement error extension)
種類	Bayesian sampling algorithm for latent-variable models	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	HMC measurement error model, Bayesian errors-in-variables with HMC, HMC latent variable measurement error, Hamiltonian MCMC with covariate error	Gibbs sampler with errors-in-variables, MCMC measurement error model, Bayesian errors-in-variables Gibbs, Gibbs EIV sampling
関連	6	5
概要	Hamiltonian Monte Carlo (HMC) with measurement error is a Bayesian computational strategy for fitting models where one or more covariates are observed with noise. HMC samples jointly from the posterior over model parameters and the unobserved true covariate values, using gradient-based proposals that explore the high-dimensional posterior efficiently and avoid the slow random-walk behaviour of standard Metropolis sampling.	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.