  We derive new models of stochastic Hall magnetohydrodynamics (MHD) by using a
symmetry-reduced stochastic Euler-Poincar\'e variational principle. The new
stochastic Hall MHD theory has potential applications for uncertainty
quantification and data assimilation in space plasma (space weather) and solar
physics. The stochastic geometric mechanics approach we take here produces
coordinate-free results which may then be applied in a variety of spatial
configurations.
