On the Difficulties of Assessing Statistical Privacy

Overview

This lecture presents two original Bayesian approaches to the quantification of statistical privacy. The first approach by Bon, Bailie, Rousseau & Robert (2026) is persuasive privacy, a framework for measuring privacy from a Bayesian game-theoretic perspective inspired by Bayesian persuasion. A data curator commits to a release mechanism, and an adversary updates her beliefs and acts on them. Privacy is then measured by how far the release can move the adversary's decisions. The framework yields new, purpose-driven privacy definitions that are rigorously justified, and it lets existing guarantees be assessed through game theory. Pure and probabilistic differential privacy do appear as special cases of this framework, the post-processing inequality receives new interpretations, and privacy guarantees can be established for deterministic algorithms, which current standards overlook. The second approach by (Bell, Johnston, Luciano & Robert (2026) is Bayesian adversarial privacy, a contextual and specific notion involving a curator, a legitimate user and an adversary. We argue it is more meaningful than differential privacy and more explicit and rigorous than the formulations common in statistical disclosure control. It also resorts to standard Bayesian decision theory but departs from it in an important respect. The party controlling the release should make disclosure decisions from the prior viewpoint, not conditional on the data, even when the data are observed. Toy examples and computational methods illustrate both approaches.