A Bayesian approach to modelling spectrometer data chromaticity corrected using beam factors -- II. Model priors and posterior odds

TL;DR

This study evaluates beam-factor chromaticity correction (BFCC) for spectrometer data in searching for the global 21-cm signal, extending beyond Paper I by testing lower-amplitude scenarios and introducing BaNTER validation to guard against biased inferences from composite foreground models. Using realistic BFCC EDGES-low simulations across null, moderate, and high signal amplitudes, the authors compare BFCC to Intrinsic, LinPhys, and MultLin foreground families and assess model validity with Bayes-factor-based model comparison and BaNTER-driven posterior odds. They demonstrate that BaNTER validation reliably identifies models that yield unbiased 21-cm signal estimates, with BFCC models having complexity $N\geq5$ and MultLin $N\geq6$ yielding the most robust, unbiased detections, while unvalidated comparisons frequently produce spurious detections or biased posteriors. The results argue that combining BFCC with BaNTER validation provides a statistically consistent framework for robust global 21-cm signal inference, informing model selection and guiding future applications to EDGES-like datasets and related cosmological analyses.

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 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. 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.

Figures (7)

• Figure 1: Astrophysical components of our simulated data sets. \ref{['Fig:ForegroundBaseMapModel']}: Our intrinsic foreground brightness temperature distribution model, evaluated at the centre of our simulated spectral band, $T_\mathrm{fg}(75~\mathrm{MHz}, l, b)$. \ref{['Fig:SImodel']}: The spatially-dependent foreground spectral index distribution $\beta(l, b)$ used when constructing simulated observational data. \ref{['Fig:Tcorrected']}: Simulated time-averaged, beam factor chromaticity corrected spectrum resulting from time-averaging simulated BFCC EDGES low-band data over 120 simulated snapshot spectra derived at 6 minute intervals in the LST range $0 \le LST < 12~\mathrm{h}$, matching the LST window of the publicly available EDGES low-band data. \ref{['Fig:T21']}: Input 21-cm signal, in the simulated BFCC data, in the three signal amplitude regimes analysed in \ref{['Sec:Results']}.
• Figure 2: Bayes factors ($\mathcal{B}_{i\mathrm{max}}$) of model $\bm{M}_{i}$ relative to the highest-evidence model $\bm{M}_{\mathrm{max}}$ for the foreground-only validation data set $\bm{D}_{\mathrm{v}}$. The parameter count $N$ denotes the number of terms in the model component with a priori unknown complexity (see main text). In the flexible-complexity BFCC and MultLin parametrisations, models that include a 21-cm signal are connected by solid lines, and those without a 21-cm signal are connected by dotted lines. In both these and the fixed-complexity Intrinsic and LinPhys models, the presence or absence of a 21-cm signal is also indicated by large and small symbols, respectively (see legend). Models with maximum total evidence in the BFCC and MultLin classes are marked by vertical dashed lines in blue and pink, respectively.
• Figure 3: Results of the Bayesian comparison of models for simulated data incorporating a moderate amplitude 21-cm signal ($A = 150~\mathrm{mK}$). Left: Bayes factors ($\mathcal{B}_{i\mathrm{max}}$) comparing model $\bm{M}_{i}$ to the maximum evidence model, $\bm{M}_\mathrm{max}$. Here, $i$ runs over all models in the set $\bm{\mathcal{M}}$, which includes both the models that pass and those that fail BaNTER validation). Right: Posterior odds ($\mathcal{R}_{i\mathrm{max}}$) of model $\bm{M}_{i}$ over the validated model $\bm{M}_\mathrm{max, v}$. Here, $\bm{M}_\mathrm{max}$ and $\bm{M}_\mathrm{max, v}$ represent the models with the highest Bayesian evidence and posterior odds, respectively. Symbols and solid and dashed lines have the same meanings as in \ref{['Fig:ForegroundOnlyBayesFactors']}. The subset of models that are present in the left panel but are absent in the right represent the set of models that failed the BaNTER null test. The number of foreground terms with the highest evidence (left) and highest posterior odds (right) for these models are indicated by blue and pink vertical, dashed lines, respectively.
• Figure 4: Signal recovery plots for models detecting a 21-cm signal in simulated data containing a moderate amplitude signal ($A=150~\mathrm{mK}$). Each subplot shows posterior probability densities of foreground-only residuals (top), full-model residuals (middle), and recovered 21-cm signal (bottom). Dotted lines in the top and middle panels indicate the noise level; the dashed black line shows the true input signal. Models are arranged by increasing Bayesian evidence (lowest evidence in top-left, highest in bottom-right). Background colours distinguish BaNTER validation results: red backgrounds indicate failed validation and blue backgrounds indicate passed validation. We highlight models using bold for highest evidence models (those with $\ln(\mathcal{B}_{i\mathrm{max}}) \geq -3$) and italic for highest BaNTER-validated posterior odds models (those with $\ln(\mathcal{R}_{i\mathrm{max}}) \geq -3$). Models meeting both criteria appear in bold italic. Subfigure captions indicate the model type and foreground complexity ($N$).
• Figure 5: As in \ref{['Fig:BandRwithAeq150mK']} but for the Bayesian comparison of models for simulated data incorporating a high amplitude 21-cm signal model ($A=500~\mathrm{mK}$).