# Uncertainty in the Dark Matter Velocity Profile

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 $m$.

##### Andrew Fowlie
###### Junior Faculty

My research interests include particle physics and statistics.