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| ベイズ一般化線形モデル× | 一般化線形モデル（GLM）× | |
|---|---|---|
| 分野 | 統計学 | 統計学 |
| 系統 | Regression model | Regression model |
| 提唱年≠ | 1989 (GLM); 1995 (Bayesian BDA) | 1972 |
| 提唱者≠ | McCullagh & Nelder (GLM framework); Bayesian treatment formalized by Gelman et al. | John A. Nelder & Robert W. M. Wedderburn |
| 種類≠ | Bayesian regression model | Regression framework |
| 原典≠ | 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 | Nelder, J. A., & Wedderburn, R. W. M. (1972). Generalized linear models. Journal of the Royal Statistical Society: Series A (General), 135(3), 370–384. DOI ↗ |
| 別名 | Bayesian GLM, Bayesian GLIM, Bayesian generalized linear regression, Bayes GLM | GLM, generalized regression, exponential family regression, link-function model |
| 関連 | 6 | 6 |
| 概要≠ | 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 Generalized Linear Model is a unified regression framework that extends ordinary linear regression to outcomes from the exponential family — including binary, count, proportion, and continuous positive outcomes. A link function connects the linear predictor to the mean of the response, enabling principled modelling beyond the Gaussian case. |
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