Linganisha mbinu

	Hamiltonian Monte Carlo yenye Hitilafu ya Kipimo	Utoaji wa Kibayesia kwa Kosa la Kipimo
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 (Bayesian formulation); Carroll et al. (comprehensive framework)
Aina	Bayesian sampling algorithm for latent-variable models	Bayesian errors-in-variables model
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: 978-1584886433
Majina mbadala	HMC measurement error model, Bayesian errors-in-variables with HMC, HMC latent variable measurement error, Hamiltonian MCMC with covariate error	Bayesian errors-in-variables model, Bayesian EIV model, Bayesian measurement error model, Bayesian misclassification model
Zinazohusiana	6	5
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.	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.