Methoden vergleichen

	Bayesian Generalisiertes Lineares Modell	Bayesian Poisson-Regression
Fachgebiet	Statistik	Statistik
Familie	Regression model	Regression model
Entstehungsjahr	1989 (GLM); 1995 (Bayesian BDA)	1989 (GLM foundation); Bayesian treatment formalized in 1990s–2000s
Urheber	McCullagh & Nelder (GLM framework); Bayesian treatment formalized by Gelman et al.	Gelman et al. (BDA); classical Poisson GLM from McCullagh & Nelder (1989)
Typ	Bayesian regression model	Bayesian generalized linear model for count data
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., 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 GLM, Bayesian GLIM, Bayesian generalized linear regression, Bayes GLM	Bayesian log-linear count model, Bayesian GLM Poisson, Poisson regression with priors, Bayesian count regression
Verwandt	6	6
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 Poisson regression models non-negative integer count outcomes using a Poisson likelihood with a log link, placing prior distributions on the regression coefficients. Posterior inference — combining prior beliefs with the data likelihood — produces full probability distributions over the coefficients rather than single-point estimates, enabling coherent uncertainty quantification and incorporation of domain knowledge.