  Direct imaging searches for exoplanets around stars detect many spurious
candidates that are in fact background field stars. To help distinguish these
from genuine companions, multi-epoch astrometry can be used to identify a
common proper motion with the host star. Although this is frequently done, many
approaches lack an appropriate model for the motions of the background
population, or do not use a statistical framework to properly quantify the
results. Here we use Gaia astrometry combined with 2MASS photometry to model
the parallax and proper motion distributions of field stars around exoplanet
host stars as a function of candidate magnitude. We develop a likelihood-based
method that compares the positions of a candidate at multiple epochs with the
positions expected under both this field star model and a co-moving companion
model. Our method propagates the covariances in the Gaia astrometry and the
candidate positions. True companions are assumed to have long periods compared
to the observational baseline, so we currently neglect orbital motion. We apply
our method to a sample of 23 host stars with 263 candidates identified in the
B-Star Exoplanet Abundance Study (BEAST) survey on VLT/SPHERE. We identify
seven candidates in which the odds ratio favours the co-moving companion model
by a factor of 100 or more. Most of these detections are based on only two or
three epochs separated by less than three years, so further epochs should be
obtained to reassess the companion probabilities. Our method is publicly
available as an open-source python package from
https://github.com/herzphi/compass to use with any data.
