  Liquid xenon time-projection chambers are the world's most sensitive
detectors for a wide range of dark matter candidates. We show that the
statistical analysis of their data can be improved by replacing detector
response Monte Carlo simulations with an equivalent deterministic calculation.
This allows the use of high-dimensional undiscretized models, yielding up to
$\sim\! 2$ times better discrimination of the dominant backgrounds. In turn,
this could significantly extend the physics reach of upcoming experiments such
as XENONnT and LZ, and bring forward a potential $5 \sigma$ dark matter
discovery by over a year.
