手法を比較

	ベイズ多項ロジスティック回帰	ベイズ一般化線形モデル
分野	統計学	統計学
系統	Regression model	Regression model
提唱年	1966 (classical); Bayesian extensions established by 1990s	1989 (GLM); 1995 (Bayesian BDA)
提唱者	Gelman et al. (Bayesian treatment); classical multinomial logit by Cox (1966)	McCullagh & Nelder (GLM framework); Bayesian treatment formalized by Gelman et al.
種類	Bayesian classification model	Bayesian regression model
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	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
別名	Bayesian polytomous logistic regression, Bayesian multinomial logit, Bayesian softmax regression, Bayesian nominal logistic regression	Bayesian GLM, Bayesian GLIM, Bayesian generalized linear regression, Bayes GLM
関連	5	6
概要	Bayesian Multinomial Logistic Regression models a nominal outcome with three or more unordered categories by placing prior distributions over the regression coefficients and updating them with data via Bayes' theorem. The result is a full posterior distribution over category probabilities for each observation, enabling principled uncertainty quantification and regularization through the prior.	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.