Methoden vergleichen

	Gibbs-Sampling mit Messfehlern	Hamiltonian Monte Carlo mit Messfehlern
Fachgebiet	Bayes-Statistik	Bayes-Statistik
Familie	Bayesian methods	Bayesian methods
Entstehungsjahr	1990–1993	2006-2011
Urheber	Gelfand & Smith (Gibbs sampler); Richardson & Gilks (measurement error extension)	Neal (2011) for HMC; Carroll et al. (2006) for measurement error framework
Typ	Bayesian MCMC sampling algorithm	Bayesian sampling algorithm for latent-variable models
Wegweisende Quelle	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.	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
Aliasnamen	Gibbs sampler with errors-in-variables, MCMC measurement error model, Bayesian errors-in-variables Gibbs, Gibbs EIV sampling	HMC measurement error model, Bayesian errors-in-variables with HMC, HMC latent variable measurement error, Hamiltonian MCMC with covariate error
Verwandt	5	6
Zusammenfassung	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.	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.