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| Bayesian Generalisiertes Lineares Modell× | Bayesian Logistic Regression× | |
|---|---|---|
| Fachgebiet≠ | Statistik | Bayes-Statistik |
| Familie≠ | Regression model | Bayesian methods |
| Entstehungsjahr≠ | 1989 (GLM); 1995 (Bayesian BDA) | 2008 |
| Urheber≠ | McCullagh & Nelder (GLM framework); Bayesian treatment formalized by Gelman et al. | Gelman, Jakulin, Pittau & Su (weakly-informative prior framework, 2008) |
| Typ≠ | Bayesian regression model | Bayesian classification model |
| Wegweisende Quelle≠ | 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 | Gelman, A., Jakulin, A., Pittau, M. G. & Su, Y.-S. (2008). A Weakly Informative Default Prior Distribution for Logistic and Other Regression Models. Annals of Applied Statistics, 2(4), 1360–1383. DOI ↗ |
| Aliasnamen≠ | Bayesian GLM, Bayesian GLIM, Bayesian generalized linear regression, Bayes GLM | bayesian binary logistic regression, bayesian classification model, Bayesian Lojistik Regresyon |
| Verwandt≠ | 6 | 3 |
| Zusammenfassung≠ | A Bayesian Generalized Linear Model (Bayesian GLM) extends the classical GLM framework by placing prior distributions on the regression coefficients and updating them with data via Bayes' theorem. This yields a full posterior distribution over parameters rather than single point estimates, enabling richer uncertainty quantification and principled incorporation of prior knowledge for any exponential-family outcome. | Bayesian logistic regression is a classification model that applies Bayesian inference to a logistic (sigmoid) likelihood for binary or multinomial outcomes. Developed within the weakly-informative prior framework formalised by Gelman, Jakulin, Pittau and Su (2008), it places a prior distribution over the coefficients and combines that prior with the data likelihood to yield a full posterior distribution for each parameter — delivering calibrated class probabilities and honest uncertainty even in small samples, rare-event settings, or cases of complete separation where frequentist maximum likelihood estimation collapses. |
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