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	Metropolis-Hastings con errore di misurazione	Inferenza Bayesiana con Errore di Misura
Campo	Bayesiano	Bayesiano
Famiglia	Bayesian methods	Bayesian methods
Anno di origine	1953 (base algorithm); 1990s (measurement-error application)	1993
Ideatore	Metropolis et al. (1953); measurement-error extension developed in the 1990s Bayesian literature	Richardson & Gilks (Bayesian formulation); Carroll et al. (comprehensive framework)
Tipo	MCMC sampling algorithm	Bayesian errors-in-variables model
Fonte seminale	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	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: 978-1584886433
Alias	MH with measurement error, Metropolis-Hastings errors-in-variables, MCMC errors-in-variables, Bayesian errors-in-variables MCMC	Bayesian errors-in-variables model, Bayesian EIV model, Bayesian measurement error model, Bayesian misclassification model
Correlati	4	5
Sintesi	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.	Bayesian inference with measurement error extends the standard Bayesian framework to situations where one or more covariates or outcomes are observed with noise or misclassification. By treating the true unobserved values as latent variables and assigning them priors, the model jointly estimates the true exposure distribution and the structural parameters of interest, propagating all uncertainty through the posterior.