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| Model bayesowski z efektami mieszanymi× | Bayesowski Model Liniowy Uogólniony× | |
|---|---|---|
| Dziedzina | Statystyka | Statystyka |
| Rodzina | Regression model | Regression model |
| Rok powstania≠ | 1990s–2000s (modern Bayesian MCMC era) | 1989 (GLM); 1995 (Bayesian BDA) |
| Twórca≠ | Gelman, Hill, and the broader Bayesian hierarchical modeling tradition | McCullagh & Nelder (GLM framework); Bayesian treatment formalized by Gelman et al. |
| Typ | Bayesian regression model | Bayesian regression model |
| Źródło pierwotne≠ | 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 |
| Inne nazwy | Bayesian multilevel model, Bayesian random effects model, Bayesian LME, Bayesian hierarchical mixed model | Bayesian GLM, Bayesian GLIM, Bayesian generalized linear regression, Bayes GLM |
| Pokrewne≠ | 5 | 6 |
| Podsumowanie≠ | 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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