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| Байєсівська модель змішаних ефектів× | Байєсівська узагальнена лінійна модель× | |
|---|---|---|
| Галузь | Статистика | Статистика |
| Родина | Regression model | Regression model |
| Рік появи≠ | 1990s–2000s (modern Bayesian MCMC era) | 1989 (GLM); 1995 (Bayesian BDA) |
| Автор методу≠ | Gelman, Hill, and the broader Bayesian hierarchical modeling tradition | McCullagh & Nelder (GLM framework); Bayesian treatment formalized by Gelman et al. |
| Тип | Bayesian regression model | Bayesian regression model |
| Основоположне джерело≠ | Gelman, A., & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891 | 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 |
| Інші назви | Bayesian multilevel model, Bayesian random effects model, Bayesian LME, Bayesian hierarchical mixed model | Bayesian GLM, Bayesian GLIM, Bayesian generalized linear regression, Bayes GLM |
| Пов'язані≠ | 5 | 6 |
| Підсумок≠ | The Bayesian mixed effects model extends the classical mixed effects framework by placing prior distributions on all parameters — fixed effects, random effect variances, and residual variance — and updating them with data to produce full posterior distributions. This provides coherent uncertainty quantification for both population-level and group-level effects simultaneously. | 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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