Linganisha mbinu

	Hamiltonian Monte Carlo yenye Hitilafu ya Kipimo	MCMC yenye Hitilafu ya Upimaji
Nyanja	Mbinu za Bayes	Mbinu za Bayes
Familia	Bayesian methods	Bayesian methods
Mwaka wa asili	2006-2011	1993
Mwanzilishi	Neal (2011) for HMC; Carroll et al. (2006) for measurement error framework	Richardson & Gilks; Carroll, Ruppert & Stefanski
Aina	Bayesian sampling algorithm for latent-variable models	Bayesian computational estimation
Chanzo asilia	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: 978-1584886334
Majina mbadala	HMC measurement error model, Bayesian errors-in-variables with HMC, HMC latent variable measurement error, Hamiltonian MCMC with covariate error	MCMC errors-in-variables, Bayesian measurement error MCMC, MCMC misclassification model, Bayesian errors-in-variables
Zinazohusiana	6	6
Muhtasari	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.	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.