Порівняння методів

	Байєсівська Пуассонівська регресія	Байєсівська узагальнена лінійна модель
Галузь	Статистика	Статистика
Родина	Regression model	Regression model
Рік появи	1989 (GLM foundation); Bayesian treatment formalized in 1990s–2000s	1989 (GLM); 1995 (Bayesian BDA)
Автор методу	Gelman et al. (BDA); classical Poisson GLM from McCullagh & Nelder (1989)	McCullagh & Nelder (GLM framework); Bayesian treatment formalized by Gelman et al.
Тип	Bayesian generalized linear model for count data	Bayesian regression model
Основоположне джерело	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
Інші назви	Bayesian log-linear count model, Bayesian GLM Poisson, Poisson regression with priors, Bayesian count regression	Bayesian GLM, Bayesian GLIM, Bayesian generalized linear regression, Bayes GLM
Пов'язані	6	6
Підсумок	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.	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.