  We present global analyses of effective Higgs portal dark matter models in
the frequentist and Bayesian statistical frameworks. Complementing earlier
studies of the scalar Higgs portal, we use GAMBIT to determine the preferred
mass and coupling ranges for models with vector, Majorana and Dirac fermion
dark matter. We also assess the relative plausibility of all four models using
Bayesian model comparison. Our analysis includes up-to-date likelihood
functions for the dark matter relic density, invisible Higgs decays, and direct
and indirect searches for weakly-interacting dark matter including the latest
XENON1T data. We also account for important uncertainties arising from the
local density and velocity distribution of dark matter, nuclear matrix elements
relevant to direct detection, and Standard Model masses and couplings. In all
Higgs portal models, we find parameter regions that can explain all of dark
matter and give a good fit to all data. The case of vector dark matter requires
the most tuning and is therefore slightly disfavoured from a Bayesian point of
view. In the case of fermionic dark matter, we find a strong preference for
including a CP-violating phase that allows suppression of constraints from
direct detection experiments, with odds in favour of CP violation of the order
of 100:1. Finally, we present DDCalc 2.0.0, a tool for calculating direct
detection observables and likelihoods for arbitrary non-relativistic effective
operators.
