方法对比

	贝叶斯序数逻辑回归	贝叶斯多项逻辑回归
领域	统计学	统计学
方法族	Regression model	Regression model
起源年份	1999	1966 (classical); Bayesian extensions established by 1990s
提出者	Johnson & Albert (1999); Bayesian proportional odds framework	Gelman et al. (Bayesian treatment); classical multinomial logit by Cox (1966)
类型	Bayesian generalized linear model	Bayesian classification model
开创性文献	Johnson, V. E., & Albert, J. H. (1999). Ordinal Data Modeling. Springer. ISBN: 978-0387987484	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
别名	Bayesian proportional odds model, Bayesian cumulative logit model, Bayesian ordered logit, Bayesian cumulative link model	Bayesian polytomous logistic regression, Bayesian multinomial logit, Bayesian softmax regression, Bayesian nominal logistic regression
相关	6	5
摘要	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.	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.