Methoden vergleichen

	Bayesian Poisson-Regression	Negative Binomial Regression
Fachgebiet	Statistik	Ökonometrie
Familie	Regression model	Regression model
Entstehungsjahr	1989 (GLM foundation); Bayesian treatment formalized in 1990s–2000s	2011
Urheber	Gelman et al. (BDA); classical Poisson GLM from McCullagh & Nelder (1989)	Hilbe (textbook treatment); generalized linear model framework
Typ	Bayesian generalized linear model for count data	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	Hilbe, J. M. (2011). Negative Binomial Regression (2nd ed.). Cambridge University Press.
Aliasnamen	Bayesian log-linear count model, Bayesian GLM Poisson, Poisson regression with priors, Bayesian count regression	NB regression, NB2 regression, negatif binom regresyonu
Verwandt	6	4
Zusammenfassung	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.	Negative Binomial Regression is a generalized linear model for count outcomes that extends Poisson regression to handle overdispersion, where the variance of the counts exceeds their mean. Developed in the GLM tradition and treated in depth by Hilbe (2011), it adds a dispersion parameter so that inference stays valid when Poisson would understate the spread of the data.