手法を比較

	ベイズ多項ロジスティック回帰	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	1966 (classical); Bayesian extensions established by 1990s	1966–1974
提唱者	Gelman et al. (Bayesian treatment); classical multinomial logit by Cox (1966)	Cox (1966); Theil (1969); formalized by McFadden (1974)
種類	Bayesian classification model	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	Agresti, A. (2002). Categorical Data Analysis (2nd ed.). Wiley-Interscience. ISBN: 978-0471360933
別名	Bayesian polytomous logistic regression, Bayesian multinomial logit, Bayesian softmax regression, Bayesian nominal logistic regression	polytomous logistic regression, softmax regression, multinomial logit, nominal logistic regression
関連	5	4
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.	Multinomial logistic regression extends binary logistic regression to outcomes with three or more unordered categories. It models the log-odds of each category relative to a chosen reference category as a linear function of the predictors, and estimates all parameters simultaneously via maximum likelihood. It is the standard choice when the dependent variable is nominal with multiple levels.