Validating posteriors obtained by an emulator when jointly-fitting mock data of the global 21-cm signal and high-z galaxy UV luminosity function

Although neural-network-based emulators enable efficient parameter estimation in 21-cm cosmology, the accuracy of such constraints is poorly understood. We employ nested sampling to fit mock data of the global 21-cm signal and high-$z$ galaxy ultraviolet luminosity function (UVLF) and compare for the first time the emulated posteriors obtained using the global signal emulator ${\tt globalemu}$ to the `true' posteriors obtained using the full model on which the emulator is trained using ${\tt ARES}$. Of the eight model parameters we employ, four control the star formation efficiency (SFE), and thus can be constrained by UVLF data, while the remaining four control UV and X-ray photon production, and the minimum virial temperature of star-forming halos ($T_{\rm min}$), and thus are uniquely probed by reionization and 21-cm measurements. For noise levels of 50 and 250 mK in the 21-cm data being jointly-fit, the emulated and `true' posteriors are consistent to within $1\sigma$. However, at lower noise levels of 10 and 25 mK, ${\tt globalemu}$ overpredicts $T_{\rm min}$ and underpredicts $\gamma_{\rm lo}$, an SFE parameter, by $\approx3-4\sigma$, while the `true' ${\tt ARES}$ posteriors capture their fiducial values within $1\sigma$. We find that jointly-fitting the mock UVLF and 21-cm data significantly improves constraints on the SFE parameters by breaking degeneracies in the ${\tt ARES}$ parameter space. Our results demonstrate the astrophysical constraints that can be expected for global 21-cm experiments for a range of noise levels from pessimistic to optimistic, and also the potential for probing redshift evolution of SFE parameters by including UVLF data.