  To quantify trade-offs between increasing demand for open data sharing and
concerns about sensitive information disclosure, statistical data privacy (SDP)
methodology analyzes data release mechanisms which sanitize outputs based on
confidential data. Two dominant frameworks exist: statistical disclosure
control (SDC), and more recent, differential privacy (DP). Despite framing
differences, both SDC and DP share the same statistical problems at its core.
For inference problems, we may either design optimal release mechanisms and
associated estimators that satisfy bounds on disclosure risk, or we may adjust
existing sanitized output to create new optimal estimators. Both problems rely
on uncertainty quantification in evaluating risk and utility. In this review,
we discuss the statistical foundations common to both SDC and DP, highlight
major developments in SDP, and present exciting open research problems in
private inference.
