  We study the strong localization of hard core bosons. Using a locator
expansion we find that in the insulator, unlike for typical fermion problems,
nearly all low-energy scattering paths come with positive amplitudes and hence
interfere constructively. As a consequence, the localization length of bosonic
excitations shrinks when the constructive interference is suppressed by a
magnetic field, entailing an exponentially large positive magnetoresistance,
opposite to and significantly stronger than the analogous effect in fermions.
Within the forward scattering approximation, we find that the lowest energy
excitations are the most delocalized. A similar analysis applied to random
field Ising models suggests that the ordering transition is due to a
delocalization initiated at zero energy rather than due to the closure of a
mobility gap in the paramagnet.
