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	Small Area Estimation (Fay-Herriot Model)	ベイズ階層モデル
分野	調査方法論	ベイズ
系統	Regression model	Bayesian methods
提唱年	1979	2006
提唱者	Robert Fay & Roger Herriot	Gelman & Hill (2006); Bayesian multilevel tradition
種類	Model-based survey estimator	hierarchical probabilistic model
原典	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.
別名	SAE, Model-Based Small Area Estimation, Area-Level Model, Küçük Alan Tahmini	multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model
関連	2	4
概要	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.