So sánh phương pháp

	Ước lượng vùng nhỏ (Mô hình Fay-Herriot)	Mô hình phân cấp Bayes	Trọng số khảo sát và hiệu chỉnh
Lĩnh vực	Phương pháp luận khảo sát	Bayes	Phương pháp luận khảo sát
Họ	Regression model	Bayesian methods	Process / pipeline
Năm ra đời	1979	2006	2010
Người khởi xướng	Robert Fay & Roger Herriot	Gelman & Hill (2006); Bayesian multilevel tradition	Sharon Lohr
Loại	Model-based survey estimator	hierarchical probabilistic model	Estimation adjustment procedure
Công trình gốc	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
Tên gọi khác	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)
Liên quan	2	4	3
Tóm tắt	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.