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| MCMC mit Messfehlern× | Hierarchische Bayes'sche Inferenz× | |
|---|---|---|
| Fachgebiet | Bayes-Statistik | Bayes-Statistik |
| Familie | Bayesian methods | Bayesian methods |
| Entstehungsjahr≠ | 1993 | 1972 (Lindley & Smith); consolidated 1995–2013 |
| Urheber≠ | Richardson & Gilks; Carroll, Ruppert & Stefanski | Lindley & Smith; Gelman et al. |
| Typ≠ | Bayesian computational estimation | Bayesian multilevel model |
| 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 & Hall/CRC. ISBN: 978-1584886334 | Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955 |
| Aliasnamen | MCMC errors-in-variables, Bayesian measurement error MCMC, MCMC misclassification model, Bayesian errors-in-variables | multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model |
| Verwandt | 6 | 6 |
| Zusammenfassung≠ | 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. | Hierarchical Bayesian inference is a probabilistic modeling framework that organises parameters into levels, placing priors on the group-level parameters and hyperpriors on the parameters governing those priors. It enables partial pooling of information across groups, balancing the extremes of treating each group as independent or merging them into a single estimate. |
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