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| Multilevel Gibbs Sampling× | Hierarchische Bayes'sche Inferenz× | |
|---|---|---|
| Fachgebiet | Bayes-Statistik | Bayes-Statistik |
| Familie | Bayesian methods | Bayesian methods |
| Entstehungsjahr≠ | 1990 | 1972 (Lindley & Smith); consolidated 1995–2013 |
| Urheber≠ | Geman & Geman (1984); applied to multilevel models by Gelfand & Smith (1990) | Lindley & Smith; Gelman et al. |
| Typ≠ | MCMC sampling algorithm | Bayesian multilevel model |
| Wegweisende Quelle≠ | Gelman, A. & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891 | 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 | hierarchical Gibbs sampler, blocked Gibbs sampling for multilevel models, multilevel MCMC via Gibbs, Gibbs sampler for mixed-effects models | multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model |
| Verwandt | 6 | 6 |
| Zusammenfassung≠ | Multilevel Gibbs sampling applies the Gibbs MCMC algorithm to hierarchical (multilevel) Bayesian models, cycling through the conditional distributions of group-level parameters and population-level hyperparameters in turn. This exploits the conditional independence structure of the hierarchy to draw exact or near-exact samples from a posterior that would otherwise be analytically intractable. | 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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