  This paper introduces a new method that embeds any Bayesian model used to
generate synthetic data and converts it into a differentially private (DP)
mechanism. We propose an alteration of the model synthesizer to utilize a
censored likelihood that induces upper and lower bounds of [$\exp(-\epsilon /
2), \exp(\epsilon / 2)$], where $\epsilon$ denotes the level of the DP
guarantee. This censoring mechanism equipped with an $\epsilon-$DP guarantee
will induce distortion into the joint parameter posterior distribution by
flattening or shifting the distribution towards a weakly informative prior. To
minimize the distortion in the posterior distribution induced by likelihood
censoring, we embed a vector-weighted pseudo posterior mechanism within the
censoring mechanism. The pseudo posterior is formulated by selectively
downweighting each likelihood contribution proportionally to its disclosure
risk. On its own, the pseudo posterior mechanism produces a weaker asymptotic
differential privacy (aDP) guarantee. After embedding in the censoring
mechanism, the DP guarantee becomes strict such that it does not rely on
asymptotics. We demonstrate that the pseudo posterior mechanism creates
synthetic data with the highest utility at the price of a weaker, aDP
guarantee, while embedding the pseudo posterior mechanism in the proposed
censoring mechanism produces synthetic data with a stronger, non-asymptotic DP
guarantee at the cost of slightly reduced utility. The perturbed histogram
mechanism is included for comparison.
