Accounting for Noise and Singularities in Bayesian Calibration Methods for Global 21-cm Cosmology Experiments

TL;DR

The paper addresses biases in calibrating global 21-cm cosmology measurements due to large dynamic ranges and instrumental noise, introducing a Bayesian framework built on noise-wave parameters for the REACH receiver. It presents three main methods to handle calibrator noise and singularities: (i) a Γ-weighted conjugate-priors approach that downweights poorly matched calibrators and mitigates singularities, (ii) a marginalised polynomial method that analytically marginalises over polynomial coefficients while sampling calibrator noise and polynomial orders, and (iii) a marginalised polynomial method augmented with a physics-informed noise model to capture frequency-dependent covariances; plus cable-correction steps. On simulated REACH-like data and real lab data, the methods achieve calibration results that are equal to or better than the conventional conjugate-priors approach, with the lab data showing significant improvements in stability and accuracy, notably calibrating to within 5% of the noise floor. The work demonstrates that robustness to singularities and flexible noise modeling are crucial for reliable 21-cm calibration and informs practical data-analysis pipelines for current and future experiments.

Abstract

Due to the large dynamic ranges involved with separating the cosmological 21-cm signal from the Cosmic Dawn from galactic foregrounds, a well-calibrated instrument is essential to avoid biases from instrumental systematics. In this paper we present three methods for calibrating a global 21-cm cosmology experiment using the noise wave parameter formalisation to characterise a low noise amplifier including a careful consideration of how calibrator temperature noise and singularities will bias the result. The first method presented in this paper builds upon the existing conjugate priors method by weighting the calibrators by a physically motivated factor, thereby avoiding singularities and normalising the noise. The second method fits polynomials to the noise wave parameters by marginalising over the polynomial coefficients and sampling the polynomial orders as parameters. The third method introduces a physically motivated noise model to the marginalised polynomial method. Running these methods on a suite of simulated datasets based on the REACH receiver design and a lab dataset, we found that our methods produced a calibration solution which is equally as or more accurate than the existing conjugate priors method when compared with an analytic estimate of the calibrator's noise. We find in the case of the measured lab dataset the conjugate priors method is biased heavily by the large noise on the shorted load calibrator, resulting in incorrect noise wave parameter fits. This is mitigated by the methods introduced in this paper which calibrate the validation source spectra to within 5% of the noise floor.

Figures (5)

• Figure 1: Diagram of the REACH calibration setup using a Dicke switch. Adapted from roqueBayesianNoiseWave2021.
• Figure 2: Summary of the three calibration methods tested on the five mock datasets and the lab dataset. Here we plot the fractional difference between the calculated noise of the calibrated validation source solution and the expected noise of the validation source. Mock datasets highlighted in red indicate datasets which include cable temperature gradients. It can be seen that while the methods perform equally for the mock datasets, we see the methods presented in this paper outperform the existing conjugate priors method on a lab dataset.
• Figure 3: Corner plot of the marginalised polynomial order posterior probabilities for the lab dataset. As the higher orders are disfavoured, we can conclude that the noise wave parameters are not being overfitted by the marginalised polynomial method.
• Figure 4: Comparison of the fitted polynomial to $T_\text{NS}$ for each calibration method for the lab dataset. The existing conjugate priors method greatly underestimates the noise source temperature while the methods presented in this paper are closer to the true value. Despite the improvement, the marginalised polynomial methods still slightly underestimate the value of $T_\text{NS}$.
• Figure 5: Comparison of the difference between the calibrated validation source spectrum and the measured validation source temperature for each calibration method for the lab dataset. While there is little residual structure in all of the spectra, the absolute calibration is best for the $\Gamma$-weighted conjugate priors method, indicative of the method's ability to constrain $T_\text{NS}$ accurately. The noise level of the residuals here are close to what we expect for the short integration time of the lab dataset.