We develop a Bayesian model–based approach to finite population estimation accounting for spatial dependence. Our innovation here is a framework that achieves inference for finite population quantities in spatial process settings. A key distinction from the small area estimation setting is that we analyze finite populations referenced by their geographic coordinates. Specifically, we consider a two‐stage sampling design in which the primary units are geographic regions, the secondary units are point‐referenced locations, and the measured values are assumed to be a partial realization of a spatial process. Estimation of finite population quantities from geostatistical models does not account for sampling designs, which can impair inferential performance, whereas design‐based estimates ignore the spatial dependence in the finite population. We demonstrate by using simulation experiments that process‐based finite population sampling models improve model fit and inference over models that fail to account for spatial correlation. Furthermore, the process‐based models offer richer inference with spatially interpolated maps over the entire region. We reinforce these improvements and demonstrate scalable inference for groundwater nitrate levels in the population of California Central Valley wells by offering estimates of mean nitrate levels and their spatially interpolated maps.
This study examines issues of Small Area Estimation that are raised by reliance on the American Community Survey (ACS), which reports tract‐level data based on much smaller samples than the decennial census long‐form that it replaced. We demonstrate the problem using a 100% transcription of microdata from the 1940 census. By drawing many samples from two major cities, we confirm a known pattern: random samples yield unbiased point estimates of means or proportions, but estimates based on smaller samples have larger average errors in measurement and greater risk of large error. Sampling variability also inflates estimates of measures of variation across areas (reflecting segregation or spatial inequality). This variation is at the heart of much contemporary spatial analysis. We then evaluate possible solutions. For point estimates, we examine three Bayesian models, all of which reduce sampling variation, and we encourage use of such models to correct ACS small area estimates. However, the corrected estimates cannot be used to calculate estimates of variation, because smoothing toward local or grand means artificially reduces variation. We note that there are potential Bayesian approaches to this problem, and we demonstrate an efficacious alternative that uses the original sample data.
more » « less- NSF-PAR ID:
- 10371794
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Geographical Analysis
- Volume:
- 52
- Issue:
- 3
- ISSN:
- 0016-7363
- Page Range / eLocation ID:
- p. 325-350
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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