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| El Model Additiu Generalitzat Bayesà (Bayesian GAM)× | Model Lineal General Bayesiana× | |
|---|---|---|
| Camp | Estadística | Estadística |
| Família | Regression model | Regression model |
| Any d'origen≠ | 1990s–2000s | 1989 (GLM); 1995 (Bayesian BDA) |
| Autor original≠ | Hastie & Tibshirani (GAM framework, 1990); Bayesian formulation developed through work by Wood, Fahrmeir, Lang, and others | McCullagh & Nelder (GLM framework); Bayesian treatment formalized by Gelman et al. |
| Tipus≠ | Semiparametric Bayesian regression | Bayesian regression model |
| Font seminal≠ | Wood, S. N. (2017). Generalized Additive Models: An Introduction with R (2nd ed.). CRC Press. ISBN: 9781498728331 | 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 |
| Àlies | Bayesian GAM, BGAM, Bayesian semiparametric regression, Bayesian smooth regression | Bayesian GLM, Bayesian GLIM, Bayesian generalized linear regression, Bayes GLM |
| Relacionats≠ | 4 | 6 |
| Resum≠ | Bayesian Generalized Additive Models extend the frequentist GAM framework by placing prior distributions over the smooth functions and any additional model parameters. This yields full posterior distributions over each smooth effect, enabling principled uncertainty quantification, automatic smoothness selection via hyperpriors, and seamless integration with hierarchical or mixed-effects structures. | 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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