Bayesian evidence-driven likelihood selection for sky-averaged 21-cm signal extraction

We demonstrate that the Bayesian evidence can be used to find a good approximation of the true likelihood function of a dataset, a goal of the likelihood-free inference (LFI) paradigm. As a concrete example, we use forward modelled sky-averaged 21-cm signal antenna temperature datasets where we artificially inject noise structures of various physically motivated forms. We find that the Gaussian likelihood performs poorly when the noise distribution deviates from the Gaussian case e.g. heteroscedastic radiometric or heavy-tailed noise. For these non-Gaussian noise structures, we show that the generalised normal likelihood is on a similar Bayesian evidence scale with comparable sky-averaged 21-cm signal recovery as the true likelihood function of our injected noise. We therefore propose the generalised normal likelihood function as a good approximation of the true likelihood function if the noise structure is a priori unknown

Bayesian evidence-driven diagnosis of instrumental systematics for sky-averaged 21-cm cosmology experiments

We demonstrate the effectiveness of a Bayesian evidence-based analysis for diagnosing and disentangling the sky-averaged 21-cm signal from instrumental systematic effects. As a case study, we consider a simulated REACH pipeline with an injected systematic. We demonstrate that very poor performance or erroneous signal recovery is achieved if the systematic remains unmodelled. These effects include sky-averaged 21-cm posterior estimates resembling a very deep or wide signal. However, when including parameterised models of the systematic, the signal recovery is dramatically improved in performance. Most importantly, a Bayesian evidence-based model comparison is capable of determining whether or not such a systematic model is needed as the true underlying generative model of an experimental dataset is in principle unknown. We, therefore, advocate a pipeline capable of testing a variety of potential systematic errors with the Bayesian evidence acting as the mechanism for detecting their presence

Effect of gain and phase errors on SKA1-low imaging quality from 50-600 MHz

Simulations of SKA1-low were performed to estimate the noise level in images produced by the telescope over a frequency range 50-600 MHz, which extends the 50-350 MHz range of the current baseline design. The root-mean-square (RMS) deviation between images produced by an ideal, error-free SKA1-low and those produced by SKA1-low with varying levels of uncorrelated gain and phase errors was simulated. The residual in-field and sidelobe noise levels were assessed. It was found that the RMS deviations decreased as the frequency increased. The residual sidelobe noise decreased by a factor of ~5 from 50 to 100 MHz, and continued to decrease at higher frequencies, attributable to wider strong sidelobes and brighter sources at lower frequencies. The thermal noise limit is found to range between ~10 - 0.3 $\mu$Jy and is reached after ~100-100 000 hrs integration, depending on observation frequency, with the shortest integration time required at ~100 MHz.Comment: 23 pages, 11 figures Typo correcte

A Bayesian approach to RFI mitigation

Interfering signals such as Radio Frequency Interference from ubiquitous satellite constellations are becoming an endemic problem in fields involving physical observations of the electromagnetic spectrum. To address this we propose a novel data cleaning methodology. Contamination is simultaneously flagged and managed at the likelihood level. It is modeled in a Bayesian fashion through a piecewise likelihood that is constrained by a Bernoulli prior distribution. The techniques described in this paper can be implemented with just a few lines of code.Comment: 6 pages, 4 figures, accepted by Physical Review D (APS

Closed-form Jones matrix of dual-polarized inverted-vee dipole antennas over lossy ground

This paper presents a closed-form expression for the Jones matrix of a dual-polarized inverted-vee dipole antenna based on the Lorentz reciprocity theorem and the basic rules of electromagnetic refraction. The expression is used to determine the intrinsic cross-polarization ratio (IXR) as a function of droop angle, position of the source in the sky, antenna height, frequency, and reflection coefficient of the underlying ground. The expression is verified using full-wave simulations with a method-of-moments solver, showing very good agreement. It explains the increase in the IXR when the antenna is placed over a perfect electric ground plane. This result is used to explain the polarization properties of the Square Kilometre Array Log-periodic Antenna. Through the LOw-Frequency ARray Low-Band Antenna (LOFAR-LBA), the importance of the size of the ground plane is explained. Finally, design consideration for high polarization purity antennas is discussed

Sky-averaged 21-cm signal extraction using multiple antennas with an SVD framework: the REACH case

In a sky-averaged 21-cm signal experiment, the uncertainty on the extracted signal depends mainly on the covariance between the foreground and 21-cm signal models. In this paper, we construct these models using the modes of variation obtained from the Singular Value Decomposition of a set of simulated foreground and 21-cm signals. We present a strategy to reduce this overlap between the 21-cm and foreground modes by simultaneously fitting the spectra from multiple different antennas, which can be used in combination with the method of utilizing the time dependence of foregrounds while fitting multiple drift scan spectra. To demonstrate this idea, we consider two different foreground models (i) a simple foreground model, where we assume a constant spectral index over the sky, and (ii) a more realistic foreground model, with a spatial variation of the spectral index. For the simple foreground model, with just a single antenna design, we are able to extract the signal with good accuracy if we simultaneously fit the data from multiple time slices. The 21-cm signal extraction is further improved when we simultaneously fit the data from different antennas as well. This improvement becomes more pronounced while using the more realistic mock observations generated from the detailed foreground model. We find that even if we fit multiple time slices, the recovered signal is biased and inaccurate for a single antenna. However, simultaneously fitting the data from different antennas reduces the bias and the uncertainty by a factor of 2-3 on the extracted 21-cm signal.Comment: 12 pages, 13 figures. Accepted for publication in MNRAS. Accompanying code is available https://github.com/anchal-009/SAVED21c