手法を比較

	ベイズ型確率モデル	ベイズ多項ロジスティック回帰
分野	統計学	統計学
系統	Regression model	Regression model
提唱年	1993	1966 (classical); Bayesian extensions established by 1990s
提唱者	Albert & Chib (data augmentation formulation)	Gelman et al. (Bayesian treatment); classical multinomial logit by Cox (1966)
種類	Binary regression (Bayesian)	Bayesian classification model
原典	Albert, J. H., & Chib, S. (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association, 88(422), 669-679.	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 probit regression, probit model with data augmentation, Gibbs sampling probit, Albert-Chib probit	Bayesian polytomous logistic regression, Bayesian multinomial logit, Bayesian softmax regression, Bayesian nominal logistic regression
関連	6	5
概要	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.	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.