手法を比較

	ベイズ型 Tobit モデル	ベイズ一般化線形モデル
分野	統計学	統計学
系統	Regression model	Regression model
提唱年	1958 (classical); 1992 (Bayesian formulation)	1989 (GLM); 1995 (Bayesian BDA)
提唱者	James Tobin (classical Tobit, 1958); Siddhartha Chib (Bayesian Tobit, 1992)	McCullagh & Nelder (GLM framework); Bayesian treatment formalized by Gelman et al.
種類	Bayesian censored/limited-dependent-variable regression	Bayesian regression model
原典	Tobin, J. (1958). Estimation of relationships for limited dependent variables. Econometrica, 26(1), 24–36.	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
別名	Bayesian censored regression, Bayesian Type I Tobit, Bayesian truncated regression, Tobit with priors	Bayesian GLM, Bayesian GLIM, Bayesian generalized linear regression, Bayes GLM
関連	5	6
概要	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.	A Bayesian Generalized Linear Model (Bayesian GLM) extends the classical GLM framework by placing prior distributions on the regression coefficients and updating them with data via Bayes' theorem. This yields a full posterior distribution over parameters rather than single point estimates, enabling richer uncertainty quantification and principled incorporation of prior knowledge for any exponential-family outcome.