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| Regressione Logistica Multinomiale Bayesiana× | Regressione Logistica Ordinale Bayesiana× | |
|---|---|---|
| Campo | Statistica | Statistica |
| Famiglia | Regression model | Regression model |
| Anno di origine≠ | 1966 (classical); Bayesian extensions established by 1990s | 1999 |
| Ideatore≠ | Gelman et al. (Bayesian treatment); classical multinomial logit by Cox (1966) | Johnson & Albert (1999); Bayesian proportional odds framework |
| Tipo≠ | Bayesian classification model | Bayesian generalized linear model |
| Fonte seminale≠ | 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 | Johnson, V. E., & Albert, J. H. (1999). Ordinal Data Modeling. Springer. ISBN: 978-0387987484 |
| Alias | Bayesian polytomous logistic regression, Bayesian multinomial logit, Bayesian softmax regression, Bayesian nominal logistic regression | Bayesian proportional odds model, Bayesian cumulative logit model, Bayesian ordered logit, Bayesian cumulative link model |
| Correlati≠ | 5 | 6 |
| Sintesi≠ | 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 ordinal logistic regression extends the classical proportional odds model by placing prior distributions on the regression coefficients and threshold parameters and updating them with observed data via Bayes' theorem. The result is a full posterior distribution over all parameters, enabling uncertainty quantification without relying on large-sample approximations. |
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