  One of the simplest viable models for dark matter is an additional neutral
scalar, stabilised by a $\mathbb{Z}_2$ symmetry. Using the GAMBIT package and
combining results from four independent samplers, we present Bayesian and
frequentist global fits of this model. We vary the singlet mass and coupling
along with 13 nuisance parameters, including nuclear uncertainties relevant for
direct detection, the local dark matter density, and selected quark masses and
couplings. We include the dark matter relic density measured by Planck, direct
searches with LUX, PandaX, SuperCDMS and XENON100, limits on invisible Higgs
decays from the Large Hadron Collider, searches for high-energy neutrinos from
dark matter annihilation in the Sun with IceCube, and searches for gamma rays
from annihilation in dwarf galaxies with the Fermi-LAT. Viable solutions remain
at couplings of order unity, for singlet masses between the Higgs mass and
about 300 GeV, and at masses above $\sim$1 TeV. Only in the latter case can the
scalar singlet constitute all of dark matter. Frequentist analysis shows that
the low-mass resonance region, where the singlet is about half the mass of the
Higgs, can also account for all of dark matter, and remains viable. However,
Bayesian considerations show this region to be rather fine-tuned.
