方法对比
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| 贝叶斯广义线性模型× | 贝叶斯概率模型× | |
|---|---|---|
| 领域 | 统计学 | 统计学 |
| 方法族 | Regression model | Regression model |
| 起源年份≠ | 1989 (GLM); 1995 (Bayesian BDA) | 1993 |
| 提出者≠ | McCullagh & Nelder (GLM framework); Bayesian treatment formalized by Gelman et al. | Albert & Chib (data augmentation formulation) |
| 类型≠ | Bayesian regression model | Binary regression (Bayesian) |
| 开创性文献≠ | 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 | Albert, J. H., & Chib, S. (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association, 88(422), 669-679. DOI ↗ |
| 别名 | Bayesian GLM, Bayesian GLIM, Bayesian generalized linear regression, Bayes GLM | Bayesian probit regression, probit model with data augmentation, Gibbs sampling probit, Albert-Chib probit |
| 相关 | 6 | 6 |
| 摘要≠ | 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. | 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. |
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