Bayesian nonparametric disclosure risk assessment

Abstract

Any decision about the release of microdata for public use is supported by the estimation of measures of disclosure risk, the most popular being the number ${\mathit{\tau }}_1$ of sample uniques that are also population uniques. In such a context, parametric and nonparametric partition-based models have been shown to have: i) the strength of leading to estimators of ${\mathit{\tau }}_1$ with desirable features, including ease of implementation, computational efficiency and scalability to massive data; ii) the weakness of producing underestimates of ${\mathit{\tau }}_1$ in realistic scenarios, with the underestimation getting worse as the tail behaviour of the empirical distribution of microdata gets heavier. To fix this underestimation phenomenon, we propose a Bayesian nonparametric partition-based model that can be tuned to the tail behaviour of the empirical distribution of microdata. Our model relies on the Pitman–Yor process prior, and it leads to a novel estimator of ${\mathit{\tau }}_1$ with all the desirable features of partition-based estimators and that, in addition, allows to reduce underestimation by tuning a “discount” parameter. We show the effectiveness of our estimator through its application to synthetic data and real data.