A microlensing search of 700 million VVV light curves
  The VISTA Variables in the Via Lactea (VVV) survey and its extension, have
been monitoring about 560 square degrees of sky centred on the Galactic bulge
and inner disc for nearly a decade. The photometric catalogue contains of order
10$^9$ sources monitored in the K$_s$ band down to 18 mag over hundreds of
epochs from 2010-2019. Using these data we develop a decision tree classifier
to identify microlensing events. As inputs to the tree, we extract a few
physically motivated features as well as simple statistics ensuring a good fit
to a microlensing model both on and off the event amplification. This produces
a fast and efficient classifier trained on a set of simulated microlensing
events and catacylsmic variables, together with flat baseline light curves
randomly chosen from the VVV data. The classifier achieves 97 per cent accuracy
in identifying simulated microlensing events in a validation set. We run the
classifier over the VVV data set and then visually inspect the results, which
produces a catalogue of 1,959 microlensing events. For these events, we provide
the Einstein radius crossing time via a Bayesian analysis. The spatial
dependence on recovery efficiency of our classifier is well characterised, and
this allows us to compute spatially resolved completeness maps as a function of
Einstein crossing time over the VVV footprint. We compare our approach to
previous microlensing searches of the VVV. We highlight the importance of
Bayesian fitting to determine the microlensing parameters for events with
surveys like VVV with sparse data.
