  We develop a novel approximate Bayesian computation (ABC) framework, ABCDP,
that produces differentially private (DP) and approximate posterior samples.
Our framework takes advantage of the Sparse Vector Technique (SVT), widely
studied in the differential privacy literature. SVT incurs the privacy cost
only when a condition (whether a quantity of interest is above/below a
threshold) is met. If the condition is met sparsely during the repeated
queries, SVT can drastically reduces the cumulative privacy loss, unlike the
usual case where every query incurs the privacy loss. In ABC, the quantity of
interest is the distance between observed and simulated data, and only when the
distance is below a threshold, we take the corresponding prior sample as a
posterior sample. Hence, applying SVT to ABC is an organic way to transform an
ABC algorithm to a privacy-preserving variant with minimal modification, but
yields the posterior samples with a high privacy level. We theoretically
analyze the interplay between the noise added for privacy and the accuracy of
the posterior samples.
