  The Gaussian mechanism is one differential privacy mechanism commonly used to
protect numerical data. However, it may be ill-suited to some applications
because it has unbounded support and thus can produce invalid numerical answers
to queries, such as negative ages or human heights in the tens of meters. One
can project such private values onto valid ranges of data, though such
projections lead to the accumulation of private query responses at the
boundaries of such ranges, thereby harming accuracy. Motivated by the need for
both privacy and accuracy over bounded domains, we present a bounded Gaussian
mechanism for differential privacy, which has support only on a given region.
We present both univariate and multivariate versions of this mechanism and
illustrate a significant reduction in variance relative to comparable existing
work.
