方法对比

	贝叶斯分位数回归	贝叶斯 Tobit 模型
领域	统计学	统计学
方法族	Regression model	Regression model
起源年份	2001–2011	1958 (classical); 1992 (Bayesian formulation)
提出者	Kozumi & Kobayashi; building on Yu & Moyeed (2001)	James Tobin (classical Tobit, 1958); Siddhartha Chib (Bayesian Tobit, 1992)
类型	Bayesian semiparametric regression	Bayesian censored/limited-dependent-variable regression
开创性文献	Kozumi, H., & Kobayashi, G. (2011). Gibbs sampling methods for Bayesian quantile regression. Journal of Statistical Computation and Simulation, 81(11), 1565–1578.	Tobin, J. (1958). Estimation of relationships for limited dependent variables. Econometrica, 26(1), 24–36.
别名	BQR, Bayesian quantile regression model, asymmetric Laplace Bayesian regression, posterior quantile regression	Bayesian censored regression, Bayesian Type I Tobit, Bayesian truncated regression, Tobit with priors
相关	6	5
摘要	Bayesian Quantile Regression estimates the full posterior distribution of regression coefficients at any chosen quantile of the outcome. By combining the asymmetric Laplace likelihood with prior distributions over the coefficients, it delivers uncertainty-quantified estimates of conditional quantiles — such as the median, the 10th, or the 90th percentile — without assuming Gaussian errors.	The Bayesian Tobit model extends Tobin's censored regression framework by replacing maximum-likelihood point estimates with a full posterior distribution over regression coefficients and error variance. By embedding Gibbs sampling with data augmentation, it produces credible intervals, handles small censored samples gracefully, and naturally incorporates prior knowledge about effect sizes.