مقایسهٔ روش‌ها

	مدل توبیت بیزی	مدل پروبیت بیزی
حوزه	آمار	آمار
خانواده	Regression model	Regression model
سال پیدایش	1958 (classical); 1992 (Bayesian formulation)	1993
پدیدآور	James Tobin (classical Tobit, 1958); Siddhartha Chib (Bayesian Tobit, 1992)	Albert & Chib (data augmentation formulation)
نوع	Bayesian censored/limited-dependent-variable regression	Binary regression (Bayesian)
منبع بنیادین	Tobin, J. (1958). Estimation of relationships for limited dependent variables. Econometrica, 26(1), 24–36.	Albert, J. H., & Chib, S. (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association, 88(422), 669-679.
نام‌های دیگر	Bayesian censored regression, Bayesian Type I Tobit, Bayesian truncated regression, Tobit with priors	Bayesian probit regression, probit model with data augmentation, Gibbs sampling probit, Albert-Chib probit
مرتبط	5	6
خلاصه	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.	The Bayesian Probit model is a binary regression method that models the probability of a binary outcome using the normal CDF (probit link) within a Bayesian framework. It assigns prior distributions to regression coefficients and updates them with observed data, yielding a full posterior distribution rather than a single point estimate. The Albert-Chib data-augmentation algorithm makes posterior sampling computationally efficient via Gibbs sampling.