  We present astrometric measurements of eleven nearby ultracool brown dwarfs
of spectral types Y and late-T, based on imaging observations from a variety of
space-based and ground-based telescopes. These measurements have been used to
estimate relative parallaxes and proper motions via maximum likelihood fitting
of geometric model curves. To compensate for the modest statistical
significance (<~ 7) of our parallax measurements we have employed a novel
Bayesian procedure for distance estimation which makes use of an a priori
distribution of tangential velocities, Vtan, assumed similar to that implied by
previous observations of T dwarfs. Our estimated distances are therefore
somewhat dependent on that assumption. Nevertheless, the results have yielded
distances for five of our eight Y dwarfs and all three T dwarfs. Estimated
distances in all cases are >~ 3 pc. In addition, we have obtained significant
estimates of Vtan for two of the Y dwarfs; both are <100 km/s, consistent with
membership in the thin disk population. Comparison of absolute magnitudes with
model predictions as a function of color shows that the Y dwarfs are
significantly redder in J-H than predicted by a cloud-free model
