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	Wariacyjna inferencja z błędem pomiaru	Bayesowska wnioskowanie z błędem pomiaru
Dziedzina	Statystyka bayesowska	Statystyka bayesowska
Rodzina	Bayesian methods	Bayesian methods
Rok powstania	2000s–2010s	1993
Twórca	Building on Blei et al. (2017) for VI and Carroll et al. (2006) for measurement error frameworks	Richardson & Gilks (Bayesian formulation); Carroll et al. (comprehensive framework)
Typ	Approximate Bayesian inference	Bayesian errors-in-variables model
Źródło pierwotne	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: 978-1584886433
Inne nazwy	VI with measurement error, variational Bayes measurement error model, VBEM with errors-in-variables, approximate Bayesian inference under measurement error	Bayesian errors-in-variables model, Bayesian EIV model, Bayesian measurement error model, Bayesian misclassification model
Pokrewne	4	5
Podsumowanie	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.	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.