  Precessing black hole-neutron star (BH-NS) binaries produce a rich
gravitational wave signal, encoding the binary's nature and inspiral
kinematics. Using the lalinference\_mcmc Markov-chain Monte Carlo parameter
estimation code, we use two fiducial examples to illustrate how the geometry
and kinematics are encoded into the modulated gravitational wave signal, using
coordinates well-adapted to precession. Even for precessing binaries, we show
the performance of detailed parameter estimation can be estimated by
"effective" estimates: comparisons of a prototype signal with its nearest
neighbors, adopting a fixed sky location and idealized two-detector network. We
use detailed and effective approaches to show higher harmonics provide nonzero
but small local improvement when estimating the parameters of precessing BH-NS
binaries. That said, we show higher harmonics can improve parameter estimation
accuracy for precessing binaries ruling out approximately-degenerate source
orientations.
  Our work illustrates quantities gravitational wave measurements can provide,
such as reliable component masses and the precise orientation of a precessing
short gamma ray burst progenitor relative to the line of sight. "Effective"
estimates may provide a simple way to estimate trends in the performance of
parameter estimation for generic precessing BH-NS binaries in next-generation
detectors. For example, our results suggest that the orbital chirp rate,
precession rate, and precession geometry are roughly-independent observables,
defining natural variables to organize correlations in the high-dimensional
BH-NS binary parameter space.
