arXiv subjects

Heidi Søgaard Christensen

Publications and source records attributed to Heidi Søgaard Christensen.

3 recordsLinked to original sources

arXiv2026

Bounds on the Posterior-to-Prior Ratios for Inclusion Belief under Bounded Differential Privacy

Differential privacy has become the standard for generating privacy-protected data releases. However, differential privacy does not translate intuitively to disclosure risk. In particular, it remains unclear how much an adversary's belief about an individual's inclusion in a dataset can change after observing a protected release. To address this question, we derive upper and lower bounds on the posterior-to-prior ratios of inclusion beliefs under bounded probabilistic and approximate differential privacy. By assuming a worst-case adversary with all-but-one auxiliary information, i.e., knowledge of all except for one of the participants in a dataset, we obtain bounds that apply to any adversary. Because these bounds may fail with non-zero probability, we study the corresponding failure probability for the Gaussian mechanism. We derive a theoretical upper limit on this probability and compare it with Monte Carlo estimates across a wide range of parameter settings. The observed failure rate is several orders of magnitude smaller than its theoretical upper limit, indicating that the latter is highly conservative. These findings suggest that the inferential privacy guarantees provided by differentially private mechanisms may be substantially stronger in practice than what is implied by the theoretical upper limit.

math.ST↗

arXiv2026

A normal-inverse-Wishart (NIW) Bayesian synthesizer for multivariate normal data with application to polygenic risk scores

Bayesian synthesis, which generates synthetic data by sampling from the posterior predictive distribution, is a popular approach for privatizing sensitive personal data. However, how attribute disclosure risk is affected by feature dimensionality, the number of individuals in the original dataset, and the amount of released synthetic information remains poorly understood. We propose a mathematically tractable Bayesian synthesizer for multivariate normal data based on a conjugate normal-inverse-Wishart prior for the mean vector and covariance matrix. The conjugate structure yields closed-form posteriors and enables direct investigation of an adversary's ability to infer records under different data and release settings. We then demonstrate several intuitive properties of synthetic data generation through several simulations. Specifically, we show that disclosure risk decreases with the size of the original dataset, but increases with the dimensionality of the feature space and the amount of synthetic information released, whether through the release of larger synthetic datasets or multiple generator realizations. Finally, the proposed synthesizer was used to generate synthetic versions of a polygenic risk score dataset, with the synthetic data exhibiting distributional properties comparable to those of the original data.

stat.ME↗

arXiv2025

A statistical note on extending Christensen's limits of agreement with the mean

Limits of agreement with the mean (LOAM) can be used for assessing agreement of continuous measurements made by different observers. Definitions of a LOAM for measuring reproducibility has been introduced under a two-way random effects model without interaction between subject and observer. Here we extend that model framework to include a subject-observer interaction, allowing the separation of residual measurement error and systematic variation in how individual observers measure specific objects. Further, our framework extends the LOAM concept to two metrics: one quantifying reproducibility and the other repeatability. We supply estimates and confidence intervals for the reproducibility and repeatibility LOAM and discuss sample size calculations and a test to compare LOAMs between two groups. To make the text self-contained for a complete agreement analysis, we additionally provide estimates and confidence intervals for the variance components.

stat.ME↗