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| Estymacja dla małych obszarów (Model Fay-Herriot)× | Modelowanie hierarchiczne bayesowskie× | |
|---|---|---|
| Dziedzina≠ | Metodologia badań sondażowych | Statystyka bayesowska |
| Rodzina≠ | Regression model | Bayesian methods |
| Rok powstania≠ | 1979 | 2006 |
| Twórca≠ | Robert Fay & Roger Herriot | Gelman & Hill (2006); Bayesian multilevel tradition |
| Typ≠ | Model-based survey estimator | hierarchical probabilistic model |
| Źródło pierwotne≠ | Fay, R. E., & Herriot, R. A. (1979). Estimates of income for small places: An application of James-Stein procedures to census data. Journal of the American Statistical Association, 74(366), 269–277. DOI ↗ | Gelman, A. & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. DOI ↗ |
| Inne nazwy≠ | SAE, Model-Based Small Area Estimation, Area-Level Model, Küçük Alan Tahmini | multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model |
| Pokrewne≠ | 2 | 4 |
| Podsumowanie≠ | Small Area Estimation (SAE) refers to statistical techniques that produce reliable estimates for subpopulations — geographical regions, demographic groups, or administrative units — where direct survey samples are too sparse to yield acceptable precision. The Fay-Herriot model, introduced by Robert Fay and Roger Herriot in 1979, is the canonical area-level SAE model. It supplements weak direct survey estimates with auxiliary covariate information through an empirical Bayes or BLUP framework, substantially reducing mean squared error for small domains. | Bayesian hierarchical modelling, popularised by Gelman and Hill (2006), is a Bayesian approach to nested data structures — such as students within schools within districts — that estimates separate parameters at each level while allowing those levels to share statistical strength through a mechanism called partial pooling. Where a classical hierarchical linear model treats group means as fixed unknown quantities, the Bayesian version places hyperprior distributions on those group means so that information flows freely across levels, producing more reliable group-level estimates whenever any individual group has few observations. |
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