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	MCMC z błędem pomiaru	Metropolis-Hastings z błędem pomiarowym
Dziedzina	Statystyka bayesowska	Statystyka bayesowska
Rodzina	Bayesian methods	Bayesian methods
Rok powstania	1993	1953 (base algorithm); 1990s (measurement-error application)
Twórca	Richardson & Gilks; Carroll, Ruppert & Stefanski	Metropolis et al. (1953); measurement-error extension developed in the 1990s Bayesian literature
Typ	Bayesian computational estimation	MCMC sampling algorithm
Źródło pierwotne	Carroll, R. J., Ruppert, D., Stefanski, L. A. & Crainiceanu, C. M. (2006). Measurement Error in Nonlinear Models: A Modern Perspective (2nd ed.). Chapman & Hall/CRC. ISBN: 978-1584886334	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	MCMC errors-in-variables, Bayesian measurement error MCMC, MCMC misclassification model, Bayesian errors-in-variables	MH with measurement error, Metropolis-Hastings errors-in-variables, MCMC errors-in-variables, Bayesian errors-in-variables MCMC
Pokrewne	6	4
Podsumowanie	MCMC with measurement error applies Markov chain Monte Carlo sampling to Bayesian models that explicitly account for the fact that covariates or outcomes are observed with error. By treating the true, unobserved values as latent variables and sampling their joint posterior alongside all other parameters, the method corrects for attenuation bias and produces valid inference even when some variables cannot be measured exactly.	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.