From ANN to BNN: Inferring Reionization Parameters using Uncertainty-aware Emulators of 21-cm Summaries

Abstract: Inferring astrophysical parameters from radio interferometric observations of the redshifted 21-cm signal from the Epoch of Reionization (EoR) is a challenging yet crucial task. The 21-cm signal from EoR is expected to be highly non-Gaussian; therefore, we need to use higher-order statistics, e.g., bispectrum. Moreover, the forward modeling of the signal and its statistics for a varying set of model parameters requires rerunning the simulations many times, which is computationally very expensive. To overcome this challenge, many artificial neural network (ANN) based emulators have been introduced, which produce the 21-cm summaries in a fraction of the time. However, ANN emulators have a drawback: they can only produce point-value predictions; thus, they fail to capture the uncertainty associated with their predictions. Therefore, when such emulators are used in the Bayesian inference pipeline, they cannot naturally propagate their prediction uncertainties to the estimated model parameters. To address this problem, we have developed Bayesian neural network (BNN) emulators for the 21-cm signal statistics, which provide the posterior distribution of the predicted signal statistics, including their prediction uncertainty. We use these BNN emulators in our Bayesian inference pipeline to infer the EoR parameters through 21-cm summaries of the mock observation of 21-cm signal with telescopic noise for $1000$ hr of SKA-LOW observation. We show that BNN emulators can capture the prediction uncertainty for the 21-cm power spectrum and bispectrum, and using these emulators in the inference pipeline provides better and tighter constraints on them. We reduced the training dataset and showed that, for smaller training datasets, BNN outperforms the ANN emulators. We also show that using the bispectrum as a summary statistic gives better constraints on EoR parameters than the power spectrum.