  We present the first application of the isosceles bispectrum to MCMC
parameter inference from the cosmic 21-cm signal. We extend the MCMC sampler
21cmMC to use the fast bispectrum code, BiFFT, when computing the likelihood.
We create mock 1000h observations with SKA1-low, using PyObs21 to account for
uv-sampling and thermal noise. Assuming the spin temperature is much higher
than that of the CMB, we consider two different reionization histories for our
mock observations: fiducial and late-reionization. For both models we find that
bias on the inferred parameter means and 1-$\sigma$ credible intervals can be
substantially reduced by using the isosceles bispectrum (calculated for a wide
range of scales and triangle shapes) together with the power spectrum (as
opposed to just using one of the statistics). We find that making the
simplifying assumption of a Gaussian likelihood with a diagonal covariance
matrix does not notably bias parameter constraints for the three-parameter
reionization model and basic instrumental effects considered here. This is true
even if we use extreme (unlikely) initial conditions which would be expected to
amplify biases. We also find that using the cosmic variance error calculated
with Monte-Carlo simulations using the fiducial model parameters whilst
assuming the late-reionization model for the simulated data also does not
strongly bias the inference. This implies we may be able to sparsely sample and
interpolate the cosmic variance error over the parameter space, substantially
reducing computational costs. All codes used in this work are
publicly-available.
