  We propose three synthetic microdata approaches to generate private tabular
survey data products for public release. We adapt a disclosure risk
based-weighted pseudo posterior mechanism to survey data with a focus on
producing tabular products under a formal privacy guarantee. Two of our
approaches synthesize the observed sample distribution of the outcome and
survey weights, jointly, such that both quantities together possess a
probabilistic differential privacy guarantee. The privacy-protected outcome and
sampling weights are used to construct tabular cell estimates and associated
standard errors to correct for survey sampling bias. The third approach
synthesizes the population distribution from the observed sample under a pseudo
posterior construction that treats survey sampling weights as fixed to correct
the sample likelihood to approximate that for the population. Each by-record
sampling weight in the pseudo posterior is, in turn, multiplied by the
associated privacy, risk-based weight for that record to create a composite
pseudo posterior mechanism that both corrects for survey bias and provides a
privacy guarantee for the observed sample. Through a simulation study and a
real data application to the Survey of Doctorate Recipients public use file, we
demonstrate that our three microdata synthesis approaches to construct tabular
products provide superior utility preservation as compared to the
additive-noise approach of the Laplace Mechanism. Moreover, all our approaches
allow the release of microdata to the public, enabling additional analyses at
no extra privacy cost.
