Bayesian Small Area Estimation

The wealth of timely and detailed information provided by sample surveys (see Survey Sampling; Finite Populations, Sampling From) attracts interest of researchers and analysts, with planned domains (see Sampling Designs in Surveys) being of primary yet clearly not exclusive inferential interest. Indeed, based on the sample data, a whole variety of subpopulations could be investigated to comprehend local needs and issues, highlight the geography of socioeconomic disparities, drive the planning and evaluation of policies, and so on. We denote by small area any geographical or demographic domain that is not planned for the survey. Counties, municipalities or states, or the groups obtained by cross- classification of age, sex, ethnicity, and region are examples. In general, we call direct an estimator solely based on the subsample of units belonging to the area of interest. Accurate design-based inference may be jeopardized by the small (or even zero) sample size of such domains, whence the terminology. Inferential interest concerns area-specific parameters, usually means, proportions, or percentiles. Typical applications include estimation of mean household income at the municipality level in poverty studies, the number of persons affected by a given disease in a given sex by age by region classification in epidemiological studies, the crop area under vines at the regional level in agricultural economics, and counts and rates for school age children under poverty at the county and school district levels for allocation of funds. To produce reliable estimates of such aggregates, we use indirect estimators that rely on auxiliary information to connect small areas through explicit or implicit models, thus borrowing strength and increasing the effective sample size. Such process is generally referred to as “small area estimation.” The article Small Area Estimation describes the nature of the problem and the different approaches. This article focuses on Bayesian models for small area estimation. We present two basic linear models and briefly discuss a number of different extensions that are easily accommodated under a Bayesian framework.