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ABSTRACT The reliable detection of the global 21-cm signal, a key tracer of Cosmic Dawn and the Epoch of Reionization, requires meticulous data modelling and robust statistical frameworks for model validation and comparison. In Paper I of this series, we presented the beam-factor-based chromaticity correction (BFCC) model for spectrometer data processed using BFCC to suppress instrumentally induced spectral structure. We demonstrated that the BFCC model, with complexity calibrated by Bayes factor-based model comparison (BFBMC), enables unbiased recovery of a 21-cm signal consistent with the one reported by The Experiment to Detect the Global Epoch of Reionization Signature (EDGES) from simulated data. Here, we extend the evaluation of the BFCC model to lower amplitude 21-cm signal scenarios where deriving reliable conclusions about a model’s capacity to recover unbiased 21-cm signal estimates using BFBMC is more challenging. Using realistic simulations of chromaticity-corrected EDGES-low spectrometer data, we evaluate three signal amplitude regimes – null, moderate, and high. We then conduct a Bayesian comparison between the BFCC model and three alternative models previously applied to 21-cm signal estimation from EDGES data. To mitigate biases introduced by systematics in the 21-cm signal model fit, we incorporate the Bayesian Null-Test-Evidence-Ratio (BaNTER) validation framework and implement a Bayesian inference workflow based on posterior odds of the validated models. The BaNTER-validated posterior-odds-based methodology presented here is general and transferable to other global 21-cm experiments employing Bayesian signal inference. We demonstrate that, unlike BFBMC alone, this approach consistently recovers 21-cm signal estimates that align with the true signal across all amplitude regimes, advancing robust global 21-cm signal detection methodologies. 

ABSTRACT Accurately accounting for spectral structure in spectrometer data induced by instrumental chromaticity on scales relevant for detection of the 21-cm signal is among the most significant challenges in global 21-cm signal analysis. In the publicly available Experiment to Detect the Global Epoch of Reionization Signature low-band data set, this complicating structure is suppressed using beam-factor-based chromaticity correction (BFCC), which works by dividing the data by a sky-map-weighted model of the spectral structure of the instrument beam. Several analyses of these data have employed models that start with the assumption that this correction is complete. However, while BFCC mitigates the impact of instrumental chromaticity on the data, given realistic assumptions regarding the spectral structure of the foregrounds, the correction is only partial. This complicates the interpretation of fits to the data with intrinsic sky models (models that assume no instrumental contribution to the spectral structure of the data). In this paper, we derive a BFCC data model from an analytical treatment of BFCC and demonstrate using simulated observations that, in contrast to using an intrinsic sky model for the data, the BFCC data model enables unbiased recovery of a simulated global 21-cm signal from beam-factor chromaticity-corrected data in the limit that the data are corrected with an error-free beam-factor model.