Privacy guarantees for general design matrices with varying sampling variances

Extend the formal differential-privacy guarantees for posterior draws from the Bayesian Fay–Herriot model to a general design matrix with area-specific, varying sampling variances.

Background

The paper derives formal Rényi differential privacy and zero-concentrated differential privacy guarantees for posterior draws from the Bayesian Fay–Herriot model under a simplifying assumption of equal sampling variances across areas. It later removes this assumption only for the special intercept-only model, obtaining exact finite-area coefficients for the sensitivity of each posterior mean.

The unresolved extension is to combine a general design matrix of area-level covariates with varying sampling variances. Such a result would broaden the applicability of the privacy analysis beyond the intercept-only setting used in the paper’s empirical applications.