Direct Parameter Inference from Global EoR Signal with Bayesian
  Statistics
  In the observation of sky-averaged HI signal from Epoch of Reionization,
model parameter inference can be a computation-intensive work, which makes it
hard to perform a direct one-stage model parameter inference by using MCMC
sampling method in Bayesian framework. Instead, a two-stage inference is
usually used, i.e., the parameters of some characteristic points on the EoR
spectrum model are first estimated, which are then used as the input to
estimate physical model parameters further. However, some previous works had
noticed that this kind of method could bias results, and it could be meaningful
to answer the question of whether it is feasible to perform direct one-stage
MCMC sampling and obtain unbiased physical model parameter estimations. In this
work, we studied this problem and confirmed the feasibility. We find that
unbiased estimations to physical model parameters can be obtained with a
one-stage direct MCMC sampling method. We also study the influence of some
factors that should be considered in practical observations to model parameter
inference. We find that a very tiny amplifier gain calibration error ($10^{-5}$
relative error) with complex spectral structures can significantly bias the
parameter estimation; the frequency-dependent antenna beam and geographical
position can also influence the results, so that should be carefully handled.
