手法を比較

	ベイズ多項ロジスティック回帰	ベイズ順序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	1966 (classical); Bayesian extensions established by 1990s	1999
提唱者	Gelman et al. (Bayesian treatment); classical multinomial logit by Cox (1966)	Johnson & Albert (1999); Bayesian proportional odds framework
種類	Bayesian classification model	Bayesian generalized linear 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	Johnson, V. E., & Albert, J. H. (1999). Ordinal Data Modeling. Springer. ISBN: 978-0387987484
別名	Bayesian polytomous logistic regression, Bayesian multinomial logit, Bayesian softmax regression, Bayesian nominal logistic regression	Bayesian proportional odds model, Bayesian cumulative logit model, Bayesian ordered logit, Bayesian cumulative link model
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.	Bayesian ordinal logistic regression extends the classical proportional odds model by placing prior distributions on the regression coefficients and threshold parameters and updating them with observed data via Bayes' theorem. The result is a full posterior distribution over all parameters, enabling uncertainty quantification without relying on large-sample approximations.