Privacy-preserving data analysis has become a central challenge in modern statistics, with
Differential Privacy (DP) emerging as the gold standard for protecting individual-level
information.

In this talk, I will present two projects at the intersection of DP and statistics. First, focusing on
privatized inference, I will introduce a general framework for privacy-preserving statistical
inference that constructs privatized interval estimators via consistent, privatized posterior
quantile estimation. I theoretically establish mean-squared error consistency for the proposed
estimators and demonstrate improved privacy-utility tradeoffs through extensive empirical
experiments.

Second, focusing on the inherent privacy guarantees provided by posterior sampling, I develop
a unified Rényi divergence framework to quantify the DP guarantees achieved "for free" when
releasing a single posterior sample.

These theoretical results substantially tighten existing conservative bounds and broaden the
class of Bayesian models for which inherent DP guarantees can be rigorously characterized.