手法を比較

	ベイズ一般化線形モデル	ベイズ型確率モデル
分野	統計学	統計学
系統	Regression model	Regression model
提唱年	1989 (GLM); 1995 (Bayesian BDA)	1993
提唱者	McCullagh & Nelder (GLM framework); Bayesian treatment formalized by Gelman et al.	Albert & Chib (data augmentation formulation)
種類	Bayesian regression model	Binary regression (Bayesian)
原典	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	Albert, J. H., & Chib, S. (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association, 88(422), 669-679.
別名	Bayesian GLM, Bayesian GLIM, Bayesian generalized linear regression, Bayes GLM	Bayesian probit regression, probit model with data augmentation, Gibbs sampling probit, Albert-Chib probit
関連	6	6
概要	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.	The Bayesian Probit model is a binary regression method that models the probability of a binary outcome using the normal CDF (probit link) within a Bayesian framework. It assigns prior distributions to regression coefficients and updates them with observed data, yielding a full posterior distribution rather than a single point estimate. The Albert-Chib data-augmentation algorithm makes posterior sampling computationally efficient via Gibbs sampling.