  We propose Bayesian methods to assess the statistical disclosure risk of data
released under zero-concentrated differential privacy, focusing on settings
with a strong hierarchical structure and categorical variables with many
levels. Risk assessment is performed by hypothesizing Bayesian intruders with
various amounts of prior information and examining the distance between their
posteriors and priors. We discuss applications of these risk assessment methods
to differentially private data releases from the 2020 decennial census and
perform simulation studies using public individual-level data from the 1940
decennial census. Among these studies, we examine how the data holder's choice
of privacy parameter affects the disclosure risk and quantify the increase in
risk when a hypothetical intruder incorporates substantial amounts of
hierarchical information.
