Working towards an optimal sampling of the 21 cm signal parameter space
  With a statistical detection of the 21 cm signal fluctuations from the Epoch
of Reionization (EoR) expected in the next few years, there is an interest in
developing robust and precise techniques to constrain the underlying
astrophysical parameters. Bayesian inference with Markov Chain Monte Carlo, or
different types of supervised learning for backward modelling (from signal to
parameters) are examples of such techniques. They usually require many
instances of forward modelling (from parameters to signal) in sampling the
parameters space, either when performing the steps of the Markov Chain or when
building a training sample for supervised learning. As forward modelling can be
costly (if performed with numerical simulations for example), we should attempt
to perform an optimal sampling according to some principle. With this goal in
mind, we present an approach based on defining a metric on the space of
observables, induced by the manner through which the modelling creates a
mapping from the parameter space onto the space of observables. This metric
bears a close connection to Jeffreys' prior from information theory. It is used
to generate a homogeneous and isotropic sampling of the signal space with two
different methods. We show that when the resulting optimized samplings, created
with 21cmFAST, are used to train a neural network we obtain a modest reduction
of the error on parameter reconstruction of ~10% (compared to a na\"ive
sampling of the same size). Excluding the borders of the parameter space
region, the improvement is more substantial, on the order of 30-40%.
