So sánh phương pháp

	Mô hình Tuyến tính Phân cấp Bayes	Hồi quy tuyến tính bội Bayes
Lĩnh vực	Thống kê	Thống kê
Họ	Regression model	Regression model
Năm ra đời	2006	1971
Người khởi xướng	Gelman & Hill (2006); Raudenbush & Bryk (2002) for frequentist HLM; Bayesian treatment consolidated by Gelman et al.	Arnold Zellner (econometric formulation); broader development by Harold Jeffreys and Gelman et al.
Loại	Bayesian multilevel linear model	Bayesian parametric regression
Công trình gốc	Gelman, A., & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891	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
Tên gọi khác	Bayesian HLM, Bayesian multilevel linear model, Bayesian random-effects linear model, Bayes hierarchical regression	Bayesian MLR, Bayesian linear regression, Bayesian multivariate regression, conjugate normal-inverse-gamma regression
Liên quan	5	6
Tóm tắt	The Bayesian Hierarchical Linear Model (Bayesian HLM) estimates linear relationships in nested or clustered data by placing prior distributions on all model parameters and updating them with observed data. It simultaneously models variation within groups and between groups, propagating uncertainty fully through posterior distributions rather than relying on asymptotic approximations.	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.