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| Bayesiansk diskriminantanalys× | Bayesian Latent Class Analysis (BLCA)× | |
|---|---|---|
| Ämnesområde | Statistik | Statistik |
| Familj | Latent structure | Latent structure |
| Ursprungsår≠ | 1964 | 1990s–2000s |
| Upphovsperson≠ | Seymour Geisser | Lazarsfeld (classical LCA); Bayesian formulation developed through Cheeseman & Stutz (1996) and Dunson & Xing (2009) |
| Typ≠ | Supervised classification / Bayesian inference | Bayesian latent variable / finite mixture model |
| Ursprungskälla≠ | Geisser, S. (1964). Posterior odds for multivariate normal classifications. Journal of the Royal Statistical Society, Series B, 26(1), 69–76. link ↗ | Dunson, D. B. & Xing, C. (2009). Nonparametric Bayes modeling of multivariate categorical data. Journal of the American Statistical Association, 104(487), 1042–1051. DOI ↗ |
| Alias | BDA, Bayesian linear discriminant analysis, Bayesian quadratic discriminant analysis, Bayesian classification | Bayesian LCA, BLCA, Bayesian mixture of multinomials, Bayesian finite mixture model |
| Närliggande≠ | 4 | 6 |
| Sammanfattning≠ | Bayesian discriminant analysis assigns observations to predefined groups by combining a multivariate Gaussian likelihood for each class with prior distributions over the class means and covariance matrices. Posterior predictive probabilities replace point-estimate decision boundaries, providing principled uncertainty quantification for classification in small or high-dimensional samples. | Bayesian latent class analysis extends classical LCA by placing prior distributions on all model parameters and using posterior inference — typically via MCMC — to classify individuals into unobserved categorical groups, quantify uncertainty around class membership, and select the number of classes in a principled, probabilistic way. |
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