Võrdle meetodeid

	Variatsiooniline inferents koos mõõteveaga	MCMC koos mõõtiveaga
Valdkond	Bayesi meetodid	Bayesi meetodid
Perekond	Bayesian methods	Bayesian methods
Tekkeaasta	2000s–2010s	1993
Looja	Building on Blei et al. (2017) for VI and Carroll et al. (2006) for measurement error frameworks	Richardson & Gilks; Carroll, Ruppert & Stefanski
Tüüp	Approximate Bayesian inference	Bayesian computational estimation
Algallikas	Blei, D. M., Kucukelbir, A., & McAuliffe, J. D. (2017). Variational inference: A review for statisticians. Journal of the American Statistical Association, 112(518), 859–877.	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
Rööpnimetused	VI with measurement error, variational Bayes measurement error model, VBEM with errors-in-variables, approximate Bayesian inference under measurement error	MCMC errors-in-variables, Bayesian measurement error MCMC, MCMC misclassification model, Bayesian errors-in-variables
Seotud	4	6
Kokkuvõte	Variational inference with measurement error is a scalable Bayesian approach that simultaneously estimates model parameters and latent true covariates when observed variables are contaminated by noise. Rather than sampling the posterior via MCMC, it finds the closest tractable distribution to the true posterior by maximising the evidence lower bound (ELBO), making it applicable to large datasets where full MCMC is too costly.	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.