Confidential data, such as electronic health records, activity data from wearable devices, and geolocation data, are becoming increasingly prevalent. Differential privacy provides a framework to conduct statistical analyses while mitigating the risk of leaking private information. Compositional data, which consist of vectors with positive components that add up to a constant, have received little attention in the differential privacy literature. This article proposes differentially private approaches for analyzing compositional data using the Dirichlet distribution. We explore several methods, including Bayesian and bootstrap procedures. For the Bayesian methods, we consider posterior inference techniques based on Markov Chain Monte Carlo, Approximate Bayesian Computation, and asymptotic approximations. We conduct an extensive simulation study to compare these approaches and make evidence-based recommendations. Finally, we apply the methodology to a data set from the American Time Use Survey.

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