Differentially private computed generation of household energy-consumption microdata for urban heat-vulnerability mapping: a computer-science evaluation of equity-audit distortion under DP budgets

Differential privacy (DP) is increasingly proposed as the mechanism by which household energy microdata can be released for climate-analytics applications such as urban heat-vulnerability mapping, yet the distortion that DP noise introduces into equity audits of those data has not been characterised formally. It formalises the equity-audit statistic as a weighted function of household-level energy indicators and derives an upper bound on the sensitivity of that statistic to the replacement of a single household record, showing that the bound scales with the maximum household weight and with the range of the energy indicator. The bound is then propagated through the Gaussian and Laplace mechanisms to obtain closed-form expressions for the noise scale required to achieve a target (ε, δ)-guarantee, and the resulting mean-squared distortion of the audit statistic is expressed as a function of ε, the number of households, and the weight concentration. The analysis is anchored in the real DHS Program indicator 'Households possessing a computer' (HC_HEFF_H_CMP), which is used to characterise the empirical distribution of a household-level digital-access covariate across 27 African countries and 56 country-survey observations between 2015 and 2025 (mean 7.893, standard deviation 5.144, minimum Guinea 1.50, maximum South Africa 22.00).