  In this proceeding, we present frequentist and Bayesian results from a global
fit of effective vector and Majorana fermion Higgs portal dark matter (DM)
models using the $\mathsf{GAMBIT}$ software. We systematically explore the
parameter space of these models using advanced sampling techniques to
simultaneously satisfy the observed DM abundance, Higgs invisible decay, and
indirect and direct detection limits. In addition, we take account of a set of
nuisance parameters arising from Standard Model, nuclear physics, DM halo and
velocity distribution. For the vector DM model viable solutions are found at
low and high vector masses. The Majorana fermion model requires a strong
preference for a CP-odd, parity-violating coupling which leads to a
momentum-suppression of the DM-nucleon cross-section. All of our results,
samples and input files are publicly available via
$\href{https://www.zenodo.org/communities/gambit-official/}{\textsf{Zenodo}}$.
