方法对比

	贝叶斯分位数回归	贝叶斯多元线性回归
领域	统计学	统计学
方法族	Regression model	Regression model
起源年份	2001–2011	1971
提出者	Kozumi & Kobayashi; building on Yu & Moyeed (2001)	Arnold Zellner (econometric formulation); broader development by Harold Jeffreys and Gelman et al.
类型	Bayesian semiparametric regression	Bayesian parametric 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.	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	BQR, Bayesian quantile regression model, asymmetric Laplace Bayesian regression, posterior quantile regression	Bayesian MLR, Bayesian linear regression, Bayesian multivariate regression, conjugate normal-inverse-gamma regression
相关	6	6
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.	Bayesian Multiple Linear Regression models a continuous outcome as a linear combination of several predictors, but instead of producing a single point estimate it yields a full posterior distribution over all regression coefficients and the error variance. This makes uncertainty quantification explicit and allows seamlessly incorporating prior knowledge from theory or previous studies.