Space-based transit search missions such as Kepler are collecting large
numbers of stellar light curves of unprecedented photometric precision and time
coverage. However, before this scientific goldmine can be exploited fully, the
data must be cleaned of instrumental artefacts. We present a new method to
correct common-mode systematics in large ensembles of very high precision light
curves. It is based on a Bayesian linear basis model and uses shrinkage priors
for robustness, variational inference for speed, and a de-noising step based on
empirical mode decomposition to prevent the introduction of spurious noise into
the corrected light curves. After demonstrating the performance of our method
on a synthetic dataset, we apply it to the first month of Kepler data. We
compare the results, which are publicly available, to the output of the Kepler
pipeline's pre-search data conditioning, and show that the two generally give
similar results, but the light curves corrected using our approach have lower
scatter, on average, on both long and short timescales. We finish by discussing
some limitations of our method and outlining some avenues for further
development. The trend-corrected data produced by our approach are publicly
available.Comment: 15 pages, 13 figures, accepted for publication in MNRA
