  Hanbury-Brown--Twiss interferometry is a technique which yields effective
widths (i.e., "HBT radii") of homogeneity regions in the fireballs produced in
heavy ion collisions. Because the initial conditions of these collisions are
stochastically fluctuating, the measured HBT radii also exhibit variation on an
event-by-event basis. However, HBT measurements have, to date, been performed
only on an ensemble-averaged basis, due to inherent limitations of finite
particle statistics. In this paper, we show that experimental measurements to
date are best characterized theoretically as weighted averages of the
event-by-event HBT radii, and we propose a new method for extracting
experimentally both the arithmetic mean and the variance of the event-by-event
distribution of HBT radii. We demonstrate the extraction of the mean and
variance of this distribution for a particular ensemble of numerically
generated events, and offer some ideas to extend and generalize the method to
enable measurement of higher moments of the HBT distribution as well.
