Selection between foreground models for global 21-cm experiments

TL;DR

This paper proposes a Bayesian model selection approach to determine the appropriate complexity of foreground models in global 21-cm experiments, balancing detection sensitivity and signal preservation.

Contribution

It introduces a Bayesian framework for selecting foreground model complexity based on data, tested with nested sampling on simplified 21-cm models.

Findings

Higher-order polynomial foreground models can be justified with limited data.

Strong evidence can distinguish models with different foreground complexities.

Complex foreground models may obscure subtle signal features.

Abstract

The precise form of the foregrounds for sky-averaged measurements of the 21-cm line during and before the epoch of reionization is unknown. We suggest that the level of complexity in the foreground models used to fit global 21-cm data should be driven by the data, under a Bayesian model selection methodology. A first test of this approach is carried out by applying nested sampling to simplified models of global 21-cm data to compute the Bayesian evidence for the models. If the foregrounds are assumed to be polynomials of order n in log-log space, we can infer the necessity to use n=4 rather than n=3 with <2h of integration with limited frequency coverage, for reasonable values of the n=4 coefficient. Using a higher-order polynomial does not necessarily prevent a significant detection of the 21-cm signal. Even for n=8, we can obtain very strong evidence distinguishing a reasonable model for the signal from a null model with 128h of integration. More subtle features of the signal may, however, be lost if the foregrounds are this complex. This is demonstrated using a simpler model for the signal that only includes absorption. The results highlight some pitfalls in trying to quantify the significance of a detection from errors on the parameters of the signal alone.