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Observations of the cosmic 21-cm power spectrum (PS) are starting to enableprecision Bayesian inference of galaxy properties and physical cosmology,during the first billion years of our Universe. Here we investigate the impactof common approximations about the likelihood used in such inferences,including: (i) assuming a Gaussian functional form; (ii) estimating the meanfrom a single realization; and (iii) estimating the (co)variance at a singlepoint in parameter space. We compare "classical" inference that uses anexplicit likelihood with simulation based inference (SBI) that estimates thelikelihood from a training set. Our forward-models include: (i) realizations ofthe cosmic 21-cm signal computed with 21cmFAST by varying UV and X-ray galaxyparameters together with the initial conditions; (ii) realizations of thetelescope noise corresponding to a 1000 h integration with SKA1-Low; (iii) theexcision of Fourier modes corresponding to a foreground-dominated, horizon"wedge". We find that the 1D PS likelihood is well described by a Gaussianaccounting for covariances between wavemodes and redshift bins (higher ordercorrelations are small). However, common approaches of estimating theforward-modeled mean and (co)variance from a random realization or at a singlepoint in parameter space result in biased and over-constrained posteriors. Ourbest results come from using SBI to fit a non-Gaussian likelihood with aGaussian mixture neural density estimator. Such SBI can be performed with up toan order of magnitude fewer simulations than classical, explicit likelihoodinference. Thus SBI provides accurate posteriors at a comparably lowcomputational cost.

Exploring the likelihood of the 21-cm power spectrum with simulation-based inference