  We present a Bayesian re-analysis of the sky-averaged 21-cm experimental data
from SARAS2 using nested sampling implemented with polychord, spectrally smooth
foreground modelling implemented with maxsmooth, detailed systematic modelling
and rapid signal emulation with globalemu. Our analysis differs from previous
analysis of the SARAS2 data through the use of a full Bayesian framework and
separate modelling of the foreground and non-smooth systematics. We use the
most up-to-date signal models including Lyman-$\alpha$ and CMB heating
parameterised by astrophysical parameters such as star formation efficiency,
X-ray heating efficiency, minimal virial circular velocity of star forming
galaxies, CMB optical depth and the low energy cutoff of the X-ray spectral
energy distribution. We consider models with an excess radio background above
the CMB produced via radio emission from early galaxies and parameterised by a
radio production efficiency. A non-smooth systematic is identified and modelled
as both a frequency damped sinusoid introduced by the electronics and
separately from the sky. The latter is modulated by the total efficiency of the
antenna and marginally favoured by the data. We consider three different models
for the noise in the data. The SARAS2 constraints on individual astrophysical
parameters are extremely weak however we identify classes of disfavoured
signals. We weakly disfavour standard astrophysical models with high
Lyman-$\alpha$ fluxes and weak heating and more confidently disfavour exotic
models with high Lyman-$\alpha$ fluxes, low X-ray efficiencies and high radio
production efficiencies in early galaxies.
