The mechanisms of the DP library (including the Laplace mechanism, the Gaussian mechanism, count, bounded sum and bounded mean) provide confidence intervals to capture the scale of the noise they add to a metric during the anonymization process.
Given a noised metric M and a confidence level 1 - alpha, the mechanisms return confidence intervals [L, R] containing the raw metric m (where m is the value after contribution bounding, but before applying noise) with a probability of at least 1 - alpha, i.e., Pr[L ≤ m ≤ R] ≥ 1 - alpha.
A particular confidence interval is purely based on M and non-personal parameters of the respective mechanism, such as epsilon, delta, sensitivities and contribution bounds. In particular, its computation does not access the raw metric m and consequently it also does not consume any privacy budget.
The confidence intervals provided by the library do not account for discrepancy due to contribution bounding.
For instance, consider a bounded sum over the raw entries [5, 5, 10, 20] with a lower bound of 0 and an upper bound of 10. The true sum is 40, but the bounded sum is 30. In this case, a confidence interval will contain m = 30 with the respective confidence level. No guarantees whether the interval also contains the true sum of 40 are given.