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| Bayes'sche Cox-Regression× | Bayesian Generalisiertes Lineares Modell× | |
|---|---|---|
| Fachgebiet | Statistik | Statistik |
| Familie | Regression model | Regression model |
| Entstehungsjahr≠ | 1972 (Cox PH); 2001 (Bayesian treatment) | 1989 (GLM); 1995 (Bayesian BDA) |
| Urheber≠ | Cox (1972) for the base model; Bayesian formulation by Sinha, Chen & Ghosh (1990s); comprehensive treatment by Ibrahim, Chen & Sinha (2001) | McCullagh & Nelder (GLM framework); Bayesian treatment formalized by Gelman et al. |
| Typ≠ | Survival regression | Bayesian regression model |
| Wegweisende Quelle≠ | Ibrahim, J. G., Chen, M.-H., & Sinha, D. (2001). Bayesian Survival Analysis. Springer. ISBN: 978-0387952772 | 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 | Bayesian Cox PH model, Bayesian proportional hazards model, Bayesian survival regression, BCox | Bayesian GLM, Bayesian GLIM, Bayesian generalized linear regression, Bayes GLM |
| Verwandt | 6 | 6 |
| Zusammenfassung≠ | Bayesian Cox regression combines the Cox proportional hazards model for time-to-event data with Bayesian inference. Instead of point estimates, it produces full posterior distributions over the hazard ratios, naturally incorporating prior knowledge and providing coherent uncertainty quantification even with small samples or informative censoring. | 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. |
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