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| Bayesowski model Tobita× | Bayesowski Model Liniowy Uogólniony× | |
|---|---|---|
| Dziedzina | Statystyka | Statystyka |
| Rodzina | Regression model | Regression model |
| Rok powstania≠ | 1958 (classical); 1992 (Bayesian formulation) | 1989 (GLM); 1995 (Bayesian BDA) |
| Twórca≠ | James Tobin (classical Tobit, 1958); Siddhartha Chib (Bayesian Tobit, 1992) | McCullagh & Nelder (GLM framework); Bayesian treatment formalized by Gelman et al. |
| Typ≠ | Bayesian censored/limited-dependent-variable regression | Bayesian regression model |
| Źródło pierwotne≠ | Tobin, J. (1958). Estimation of relationships for limited dependent variables. Econometrica, 26(1), 24–36. DOI ↗ | 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 |
| Inne nazwy | Bayesian censored regression, Bayesian Type I Tobit, Bayesian truncated regression, Tobit with priors | Bayesian GLM, Bayesian GLIM, Bayesian generalized linear regression, Bayes GLM |
| Pokrewne≠ | 5 | 6 |
| Podsumowanie≠ | 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. |
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