方法对比

	贝叶斯多项逻辑回归	贝叶斯逻辑回归
领域	统计学	贝叶斯
方法族	Regression model	Bayesian methods
起源年份	1966 (classical); Bayesian extensions established by 1990s	2008
提出者	Gelman et al. (Bayesian treatment); classical multinomial logit by Cox (1966)	Gelman, Jakulin, Pittau & Su (weakly-informative prior framework, 2008)
类型	Bayesian classification model	Bayesian classification model
开创性文献	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., Jakulin, A., Pittau, M. G. & Su, Y.-S. (2008). A Weakly Informative Default Prior Distribution for Logistic and Other Regression Models. Annals of Applied Statistics, 2(4), 1360–1383.
别名	Bayesian polytomous logistic regression, Bayesian multinomial logit, Bayesian softmax regression, Bayesian nominal logistic regression	bayesian binary logistic regression, bayesian classification model, Bayesian Lojistik Regresyon
相关	5	3
摘要	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 logistic regression is a classification model that applies Bayesian inference to a logistic (sigmoid) likelihood for binary or multinomial outcomes. Developed within the weakly-informative prior framework formalised by Gelman, Jakulin, Pittau and Su (2008), it places a prior distribution over the coefficients and combines that prior with the data likelihood to yield a full posterior distribution for each parameter — delivering calibrated class probabilities and honest uncertainty even in small samples, rare-event settings, or cases of complete separation where frequentist maximum likelihood estimation collapses.