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| Hamiltonian Monte Carlo mit Messfehlern× | Variationelle Inferenz bei Messfehlern× | |
|---|---|---|
| Fachgebiet | Bayes-Statistik | Bayes-Statistik |
| Familie | Bayesian methods | Bayesian methods |
| Entstehungsjahr≠ | 2006-2011 | 2000s–2010s |
| Urheber≠ | Neal (2011) for HMC; Carroll et al. (2006) for measurement error framework | Building on Blei et al. (2017) for VI and Carroll et al. (2006) for measurement error frameworks |
| Typ≠ | Bayesian sampling algorithm for latent-variable models | Approximate Bayesian inference |
| Wegweisende Quelle≠ | 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 | 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. DOI ↗ |
| Aliasnamen | HMC measurement error model, Bayesian errors-in-variables with HMC, HMC latent variable measurement error, Hamiltonian MCMC with covariate error | VI with measurement error, variational Bayes measurement error model, VBEM with errors-in-variables, approximate Bayesian inference under measurement error |
| Verwandt≠ | 6 | 4 |
| Zusammenfassung≠ | 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. | 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. |
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