Statistical modelling under differential privacy constraints: a case study in fine-scale geographical analysis with Australian Bureau of Statistics TableBuilder data

Abstract

ABSTRACT Consistent with the principles of differential privacy protection, the Australian Bureau of Statistics artificially perturbs all count data from the Australian Census prior to its release to researchers through the TableBuilder platform. This perturbation involves the addition of random noise to every non-zero cell count followed by the suppression of small values to zero. A consequent problem encountered by researchers working with geographical TableBuilder outputs is that the aggregate sums of cell counts over fine-scale units are often much lower than the direct query totals of their coarser enclosing units. Hierarchical Bayesian modelling is here proposed as a powerful methodology for achieving consistent multi-scale statistical reconstructions suitable for downstream spatial modelling. The utility of this framework is demonstrated for the toy problem of reconstructing Multiple Family Household counts by Mesh Block in the Perth Greater Capital City area.