Linganisha mbinu

	MCMC yenye Hitilafu ya Upimaji	Utoaji wa Kibayesia kwa Kosa la Kipimo
Nyanja	Mbinu za Bayes	Mbinu za Bayes
Familia	Bayesian methods	Bayesian methods
Mwaka wa asili	1993	1993
Mwanzilishi	Richardson & Gilks; Carroll, Ruppert & Stefanski	Richardson & Gilks (Bayesian formulation); Carroll et al. (comprehensive framework)
Aina	Bayesian computational estimation	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 & 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	MCMC errors-in-variables, Bayesian measurement error MCMC, MCMC misclassification model, Bayesian errors-in-variables	Bayesian errors-in-variables model, Bayesian EIV model, Bayesian measurement error model, Bayesian misclassification model
Zinazohusiana	6	5
Muhtasari	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.	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.