Linganisha mbinu

	Regression ya Kiasi ya Bayesian	UREMBA WA KIMAANDIKIO WA KIBAYESIA WA KISASA
Nyanja	Takwimu	Takwimu
Familia	Regression model	Regression model
Mwaka wa asili	2001–2011	1971
Mwanzilishi	Kozumi & Kobayashi; building on Yu & Moyeed (2001)	Arnold Zellner (econometric formulation); broader development by Harold Jeffreys and Gelman et al.
Aina	Bayesian semiparametric regression	Bayesian parametric regression
Chanzo asilia	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
Majina mbadala	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
Zinazohusiana	6	6
Muhtasari	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.