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	Próbkowanie Gibbsa z błędem pomiarowym	Metropolis-Hastings z błędem pomiarowym
Dziedzina	Statystyka bayesowska	Statystyka bayesowska
Rodzina	Bayesian methods	Bayesian methods
Rok powstania	1990–1993	1953 (base algorithm); 1990s (measurement-error application)
Twórca	Gelfand & Smith (Gibbs sampler); Richardson & Gilks (measurement error extension)	Metropolis et al. (1953); measurement-error extension developed in the 1990s Bayesian literature
Typ	Bayesian MCMC sampling algorithm	MCMC sampling algorithm
Źródło pierwotne	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
Inne nazwy	Gibbs sampler with errors-in-variables, MCMC measurement error model, Bayesian errors-in-variables Gibbs, Gibbs EIV sampling	MH with measurement error, Metropolis-Hastings errors-in-variables, MCMC errors-in-variables, Bayesian errors-in-variables MCMC
Pokrewne	5	4
Podsumowanie	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.	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.