Bayesian Downscaling Methods for Aggregated Count Data

Abstract

Policy-critical, micro-level statistical data are often unavailable at the desired level of disaggregation. We present a Bayesian methodology for “downscaling” aggregated count data to the micro level, using an outside statistical sample. Our procedure combines numerical simulation with exact calculation of combinatorial probabilities. We motivate our approach with an application estimating the number of farms in a region, using count totals at higher levels of aggregation. In a simulation analysis over varying population sizes, we demonstrate both robustness to sampling variability and outperformance relative to maximum likelihood. Spatial considerations, implementation of “informative” priors, non-spatial classification problems, and best practices are discussed.