  We propose two synthetic microdata approaches to generate private tabular
survey data products for public release. We adapt a pseudo posterior mechanism
that downweights by-record likelihood contributions with weights $\in [0,1]$
based on their identification disclosure risks to producing tabular products
for survey data. Our method applied to an observed survey database achieves an
asymptotic global probabilistic differential privacy guarantee. Our two
approaches synthesize the observed sample distribution of the outcome and
survey weights, jointly, such that both quantities together possess a privacy
guarantee. The privacy-protected outcome and survey weights are used to
construct tabular cell estimates (where the cell inclusion indicators are
treated as known and public) and associated standard errors to correct for
survey sampling bias. Through a real data application to the Survey of
Doctorate Recipients public use file and simulation studies motivated by the
application, we demonstrate that our two microdata synthesis approaches to
construct tabular products provide superior utility preservation as compared to
the additive-noise approach of the Laplace Mechanism. Moreover, our approaches
allow the release of microdata to the public, enabling additional analyses at
no extra privacy cost.
