  A recently proposed phase-estimation protocol that is based on measuring the
parity of a two-mode squeezed-vacuum state at the output of a Mach-Zehnder
interferometer shows that Cram\'{e}r-Rao bound sensitivity can be obtained [P.\
M.\ Anisimov, et al., Phys.\ Rev.\ Lett.\ {\bf104}, 103602 (2010)]. This
sensitivity, however, is expected in the case of an infinite number of parity
measurements made on an infinite number of photons. Here we consider the case
of a finite number of parity measurements and a finite number of photons,
implemented with photon-number-resolving detectors. We use Bayesian analysis to
characterize the sensitivity of the phase estimation in this scheme. We have
found that our phase estimation becomes biased near 0 or $\pi/2$ phase values.
Yet there is an in-between region where the bias becomes negligible. In this
region, our phase estimation scheme saturates the Cram\'{e}r-Rao bound and
beats the shot-noise limit.
