  Parameter estimation in statistics and system identification relies on data
that may contain sensitive information. To protect this sensitive information,
the notion of \emph{differential privacy} (DP) has been proposed, which
enforces confidentiality by introducing randomization in the estimates.
Standard algorithms for differentially private estimation are based on adding
an appropriate amount of noise to the output of a traditional point estimation
method. This leads to an accuracy-privacy trade off, as adding more noise
reduces the accuracy while increasing privacy. In this paper, we propose a new
Unified Bayes Private Point (UBaPP) approach to Bayes point estimation of the
unknown parameters of a data generating mechanism under a DP constraint, that
achieves a better accuracy-privacy trade off than traditional approaches. We
verify the performance of our approach on a simple numerical example.
