  We investigate the effect of diagonal disorder on bosons in an optical
lattice described by an Anderson-Hubbard model at zero temperature. It is known
that within Gutzwiller mean-field theory spatially resolved calculations suffer
particularly from finite system sizes in the disordered case, while arithmetic
averaging of the order parameter cannot describe the Bose glass phase for
finite hopping $J>0$. Here we present and apply a new \emph{stochastic}
mean-field theory which captures localization due to disorder, includes
non-trivial dimensional effects beyond the mean-field scaling level and is
applicable in the thermodynamic limit. In contrast to fermionic systems, we
find the existence of a critical hopping strength, above which the system
remains superfluid for arbitrarily strong disorder.
