  When releasing outputs from confidential data, agencies need to balance the
analytical usefulness of the released data with the obligation to protect data
subjects' confidentiality. For releases satisfying differential privacy, this
balance is reflected by the privacy budget, $\varepsilon$. We provide a
framework for setting $\varepsilon$ based on its relationship with Bayesian
posterior probabilities of disclosure. The agency responsible for the data
release decides how much posterior risk it is willing to accept at various
levels of prior risk, which implies a unique $\varepsilon$. Agencies can
evaluate different risk profiles to determine one that leads to an acceptable
trade-off in risk and utility.
