Compara mètodes

	Metropolis-Hastings amb error de mesura	Monte Carlo Hamiltonià amb Error de Mesura
Camp	Bayesià	Bayesià
Família	Bayesian methods	Bayesian methods
Any d'origen	1953 (base algorithm); 1990s (measurement-error application)	2006-2011
Autor original	Metropolis et al. (1953); measurement-error extension developed in the 1990s Bayesian literature	Neal (2011) for HMC; Carroll et al. (2006) for measurement error framework
Tipus	MCMC sampling algorithm	Bayesian sampling algorithm for latent-variable models
Font seminal	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 and Hall/CRC. ISBN: 978-1584886334
Àlies	MH with measurement error, Metropolis-Hastings errors-in-variables, MCMC errors-in-variables, Bayesian errors-in-variables MCMC	HMC measurement error model, Bayesian errors-in-variables with HMC, HMC latent variable measurement error, Hamiltonian MCMC with covariate error
Relacionats	4	6
Resum	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.	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.