Direct detection experiments search for dark matter in interactions with detectors on earth. The relative velocity of dark matter with respect to the detectors is, however, unknown. In [1], we pioneered the use of Quantified Maximum Entropy (see e.g., Skilling) to model the uncertainty in the velocity distribution and applied it to DAMA/LIBRA. In [2] we developed a novel numerical approximation and applied it to XENON1T.

In both works, we constructed an entropic prior for the velocity distribution, $$ p(f) \propto e^{\beta S[f, m]}, $$ where $\beta$ is a hyperparameter governing the strength of our belief in the default distribution, $m$, and $$ S[f, m] = \int f(v) \ln\left(\frac{f(v)}{m(v)}\right) dv $$ is the relative entropy between the distributions $f$ and $m$.