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| Regresja logistyczna bayesowska wielomianowa× | Regresja logistyczna bayesowska× | |
|---|---|---|
| Dziedzina≠ | Statystyka | Statystyka bayesowska |
| Rodzina≠ | Regression model | Bayesian methods |
| Rok powstania≠ | 1966 (classical); Bayesian extensions established by 1990s | 2008 |
| Twórca≠ | Gelman et al. (Bayesian treatment); classical multinomial logit by Cox (1966) | Gelman, Jakulin, Pittau & Su (weakly-informative prior framework, 2008) |
| Typ | Bayesian classification model | Bayesian classification model |
| Źródło pierwotne≠ | 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 | Gelman, A., Jakulin, A., Pittau, M. G. & Su, Y.-S. (2008). A Weakly Informative Default Prior Distribution for Logistic and Other Regression Models. Annals of Applied Statistics, 2(4), 1360–1383. DOI ↗ |
| Inne nazwy≠ | Bayesian polytomous logistic regression, Bayesian multinomial logit, Bayesian softmax regression, Bayesian nominal logistic regression | bayesian binary logistic regression, bayesian classification model, Bayesian Lojistik Regresyon |
| Pokrewne≠ | 5 | 3 |
| Podsumowanie≠ | Bayesian Multinomial Logistic Regression models a nominal outcome with three or more unordered categories by placing prior distributions over the regression coefficients and updating them with data via Bayes' theorem. The result is a full posterior distribution over category probabilities for each observation, enabling principled uncertainty quantification and regularization through the prior. | Bayesian logistic regression is a classification model that applies Bayesian inference to a logistic (sigmoid) likelihood for binary or multinomial outcomes. Developed within the weakly-informative prior framework formalised by Gelman, Jakulin, Pittau and Su (2008), it places a prior distribution over the coefficients and combines that prior with the data likelihood to yield a full posterior distribution for each parameter — delivering calibrated class probabilities and honest uncertainty even in small samples, rare-event settings, or cases of complete separation where frequentist maximum likelihood estimation collapses. |
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