Comparison of Bayesian inference methods using the LORELI II database of hydro-radiative simulations of the 21-cm signal

While the observation of the 21-cm signal from the cosmic dawn and epoch of reionisation is an instrumental challenge, the interpretation of a prospective detection is still open to questions regarding the modelling of the signal and the Bayesian inference techniques that bridge the gap between theory and observations. To address some of these questions, we present L<ns0:sc>ORELI</ns0:sc> II, a database of nearly 10 000 simulations of the 21-cm signal run with the Licorice 3D radiative transfer code. With L<ns0:sc>ORELI</ns0:sc> II, we explored a five-dimensional astrophysical parameter space where star formation, X-ray emissions, and UV emissions are varied. We then used this database to train neural networks and perform Bayesian inference on 21-cm power spectra affected by thermal noise at the level of 100 hours of observation with the Square Kilometre Array. We studied and compared three inference techniques: an emulator of the power spectrum, a neural density estimator that fits the implicit likelihood of the model, and a Bayesian neural network that directly fits the posterior distribution. We measured the performance of each method by comparing them on a statistically representative set of inferences, notably using the principles of simulation-based calibration. We report errors on the 1D marginalised posteriors (biases and over or under confidence) below 15% of the standard deviation for the emulator and below 25% for the other methods. We conclude that at our noise level and our sampling density of the parameter space, an explicit Gaussian likelihood is sufficient. This may not be the case at a lower noise level or if a denser sampling is used to reach higher accuracy. We then applied the emulator method to recent HERA upper limits and report weak constraints on the X-ray emissivity parameter of our model.