  An efficient Bayesian technique for estimation problems in fundamental
stellar astronomy is tested on simulated data for a binary observed both
astrometrically and spectroscopically. Posterior distributions are computed for
the components' masses and for the binary's parallax. One thousand independent
repetitions of the simulation demonstrate that the 1- and 2-$\!\sigma$
credibility intervals for these fundamental quantities have close to the
correct coverage fractions. In addition, the simulations allow the
investigation of the statistical properties of a Bayesian goodness-of-fit
criterion and of the corresponding p-value. The criterion has closely similar
properties to the traditional chi^{2} test for minimum-chi^{2} solutions.
