Bayesian Methods to Manage and Reduce Differential Privacy Uncertainty

Keywords: Life Expectancy, U.S. Census, Differential Privacy, Small Areas
Abstract Type: Paper Abstract

Abstract

The decennial census which is administered to every household in the United States provides policy-makers, researchers, and various public and private entities with high-quality geographic and demographics information. Differential privacy (DP) is the process by which random error is introduced into public facing census data products. Population counts, the underlying denominators of LE calculations, are intentionally infused with error by DP. Age-specific population counts in small areas (such census tracts) will be distorted, obscuring LE spatial health patterns and trends. This study examines frequentist and Bayesian spatial regression methods as potential means of correcting for and stabilizing small area LE estimates. We leverage the predictive capacity of repeated measurements of the tract itself and the spatial information of adjacent neighbors, to stabilize imprecise small area LE estimates. Correlation coefficients compared LE calculated from the original (non-DP) age-specific population counts, the DP age-specific population counts, and the removed unstable LE estimates that were statistically imputed by the spatial regression models. Consistent with previous studies, there was substantial variation in the DP 2010 population and 2010 official counts. Of the models that were examined, the Besag, York, and Mollié model (BYM) exhibited the highest correlation coefficient (0.79) of the spatial statistical models used to compare LE estimates between the original (non-DP) and the methods to manage and reduce uncertainty for unstable LE produced by DP age-specific population counts.