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 < 2 \mathrm { h } 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 128 \mathrm { h } 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 .