方法对比

	贝叶斯概率模型	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	1993	1966 (classical); Bayesian extensions established by 1990s
提出者	Albert & Chib (data augmentation formulation)	Gelman et al. (Bayesian treatment); classical multinomial logit by Cox (1966)
类型	Binary regression (Bayesian)	Bayesian classification model
开创性文献	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
别名	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
相关	6	5
摘要	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.