  We will provide bounds on both the Betti numbers and the torsion part of the
homology of hyperbolic orbifolds. These bounds are linear in the volume and are
a direct consequence of an efficient simplicial model of the thick part, which
we will construct as well. The homology statements complement previous work of
Bader, Gelander and Sauer (torsion homology of manifolds), Samet (Betti numbers
of orbifolds) and a classical theorem of Gromov (Betti numbers of manifolds).
  For arithmetic, non-compact hyperbolic orbifolds -- i.e. in the case of
arithmetic, non-uniform lattices in $\operatorname{Isom}(\mathbb{H}^n)$ -- the
strongest results will be obtained.
