  Astrophysical uncertainties in dark matter direct detection experiments are
typically addressed by parametrizing the velocity distribution in terms of a
few uncertain parameters that vary around some central values. Here we propose
a method to optimize over all velocity distributions lying within a given
distance measure from a central distribution. We discretize the dark matter
velocity distribution as a superposition of streams, and use a variety of
information divergences to parametrize its uncertainties. With this, we bracket
the limits on the dark matter-nucleon and dark matter-electron scattering cross
sections, when the true dark matter velocity distribution deviates from the
commonly assumed Maxwell-Boltzmann form. The methodology pursued is general and
could be applied to other physics scenarios where a given physical observable
depends on a function that is uncertain.
