Methoden vergleichen

	Bayesian Negative Binomial Regression	Bayesian Poisson-Regression
Fachgebiet	Statistik	Statistik
Familie	Regression model	Regression model
Entstehungsjahr	1990s–2000s	1989 (GLM foundation); Bayesian treatment formalized in 1990s–2000s
Urheber	Gelman, Carlin, Stern, Dunson, Vehtari & Rubin; Cameron & Trivedi	Gelman et al. (BDA); classical Poisson GLM from McCullagh & Nelder (1989)
Typ	Bayesian GLM for overdispersed counts	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 NB regression, Bayesian negbin model, Bayesian overdispersed count regression, Bayesian NB-2 model	Bayesian log-linear count model, Bayesian GLM Poisson, Poisson regression with priors, Bayesian count regression
Verwandt	6	6
Zusammenfassung	Bayesian Negative Binomial Regression models non-negative integer count outcomes that exhibit overdispersion — where the variance exceeds the mean — by placing a negative binomial likelihood on the data and specifying prior distributions over the regression coefficients and the dispersion parameter. Posterior inference is typically performed via Markov chain Monte Carlo (MCMC) or variational methods, yielding full posterior distributions rather than point estimates.	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.