方法对比

	贝叶斯简单线性回归	贝叶斯分位数回归
领域	统计学	统计学
方法族	Regression model	Regression model
起源年份	Early 19th century; textbook synthesis 2013	2001–2011
提出者	Laplace, P.-S. (early 19th c.); modern treatment: Gelman et al.	Kozumi & Kobayashi; building on Yu & Moyeed (2001)
类型	Bayesian linear regression	Bayesian semiparametric regression
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	Kozumi, H., & Kobayashi, G. (2011). Gibbs sampling methods for Bayesian quantile regression. Journal of Statistical Computation and Simulation, 81(11), 1565–1578.
别名	Bayesian SLR, Bayesian univariate regression, probabilistic simple linear regression, Bayesian linear model	BQR, Bayesian quantile regression model, asymmetric Laplace Bayesian regression, posterior quantile regression
相关	6	6
摘要	Bayesian Simple Linear Regression models the relationship between a continuous outcome and a single predictor by combining a Gaussian likelihood with prior distributions over the intercept, slope, and error variance. The result is a full posterior distribution over all parameters, providing probabilistic uncertainty quantification rather than a single point estimate.	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.