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	Stima per Piccole Aree (Modello di Fay-Herriot)	Modello Gerarchico Bayesiano	Ponderazione e Calibrazione delle Indagini Campionarie
Campo	Metodologia delle indagini	Bayesiano	Metodologia delle indagini
Famiglia	Regression model	Bayesian methods	Process / pipeline
Anno di origine	1979	2006	2010
Ideatore	Robert Fay & Roger Herriot	Gelman & Hill (2006); Bayesian multilevel tradition	Sharon Lohr
Tipo	Model-based survey estimator	hierarchical probabilistic model	Estimation adjustment procedure
Fonte seminale	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.	Gelman, A. & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.	Lohr, S. L. (2010). Sampling: Design and Analysis (2nd ed.). Brooks/Cole. ISBN: 978-0-495-10527-5
Alias	SAE, Model-Based Small Area Estimation, Area-Level Model, Küçük Alan Tahmini	multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model	Survey Calibration, Post-Stratification Weighting, Raking Adjustment, Ağırlıklandırma (Anket)
Correlati	2	4	3
Sintesi	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.	Survey weighting is a statistical procedure that assigns a numeric weight to each sampled unit so that the weighted sample reproduces known population totals. Rooted in classical sampling theory and systematically synthesized by Sharon Lohr (2010), the approach corrects for unequal selection probabilities, unit nonresponse, and coverage gaps, producing estimates that are more representative of the target population than raw sample means or totals would be.