Bayesian model comparison and validation with Gaussian Process Regression for interferometric 21-cm signal recovery

TL;DR

This paper tackles the challenge of extracting the faint 21-cm signal from cosmic dawn and reionization data in the presence of bright foregrounds by proposing a Bayesian model-comparison framework for Gaussian Process Regression (GPR). It introduces a variational autoencoder (VAE) kernel to capture realistic 21-cm covariance and evaluates five GPR models against realistic SKA-Low-like simulations using nested sampling to obtain global evidences and posterior distributions. A novel Bayesian null-test (BaNTER) validates model reliability by testing against data lacking a cosmological signal. The results show that wedge-parametrized models with noise scaling (notably αNoise) provide the strongest evidence and most accurate, unbiased 21-cm recovery, while some alternative models risk biased reconstructions, underscoring the need for rigorous model selection and validation in future SKA analyses.

Abstract

The 21-cm signal from neutral hydrogen is anticipated to reveal critical insights into the formation of early cosmic structures during the Cosmic Dawn and the subsequent Epoch of Reionization. However, the intrinsic faintness of the signal, as opposed to astrophysical foregrounds, poses a formidable challenge for its detection. Motivated by the recent success of machine learning based Gaussian Process Regression (GPR) methods in LOFAR and NenuFAR observations, we perform a Bayesian comparison among five GPR models to account for the simulated 4-hour tracking observations with the SKA-Low telescope. The simulated sky is convolved with the instrumental beam response and includes realistic radio sources and thermal noise from 122 to 134 MHz. A Bayesian model evaluation framework is applied to five GPR models to discern the most effective modelling strategy and determine the optimal model parameters. The GPR model with wedge parametrization ($\textit{Wedge}$) and its extension ($α\textit{Noise}$) with noise scaling achieve the highest Bayesian evidence of the observed data and the least biased 21-cm power spectrum recovery. The $α\textit{Noise}$ and $\textit{Wedge}$ models also forecast the best local power-spectrum recovery, demonstrating fractional differences of $-0.14\%$ and $0.47\%$ respectively, compared to the injected 21-cm power at $k = 0.32\ \mathrm{h\ cMpc}^{-1}$. We additionally perform Bayesian null tests to validate the five models, finding that the two optimal models also pass with the remaining three models yielding spurious detections in data containing no 21-cm signal.

Figures (17)

• Figure 1: The position layout is shown for the telescope model used in the OSKAR simulation, provided by 2025arXiv250311740B. Left panel: the geographical locations in longitude and latitude are shown for the expected SKA1-Low configuration of the 512 stations 2017MNRAS.465.3680M. The stations are arranged in a "Vogel" layout. Right panel: the relative positions are shown for the 256 antenna elements within a station. Each station is treated as identical and the beam response is simulated for a single station and duplicated for the entire 512 stations.
• Figure 2: Discrete radio sources from the GLEAM survey are shown in a natural deconvolved image at the lowest frequency of 122 MHz. The image covers 9.1° of the sky at resolution of 32 arcsec. The deconvolution leads to a better (Gaussian) PSF shape. The sources that fall outside the primary beam as defined in Equation \ref{['eq:inner_sky_patch']} are attenuated in flux density to mimic the demixing process and to balance the side-lobe amplitude from beam duplication.
• Figure 3: Diffuse radio sources from GSM, in the same frequency range, imaging resolution and FoV as in Figure \ref{['fig:gleam']}. The ring surrounding the GSM sources shows the boundary between the outer and inner sky model.
• Figure 4: The 21-cm brightness temperature fluctuations generated with 21cmFAST, in the same frequency range, imaging resolution and FoV as in Figure \ref{['fig:gleam']}. The cosmological signal is generated by using the astrophysical parameters listed in Table \ref{['sec:sky model']}.
• Figure 5: Thermal noise of the interferometric array given the layout shown in Figure \ref{['fig:ska_station_layout']}, in the same frequency range, imaging resolution and FoV as in Figure \ref{['fig:gleam']}. The noise is randomly sampled from a Gaussian distribution with its standard deviation determined by the instrumental sensitivity at each frequency.