  Cosmic Dawn (CD) and Epoch of Reionization (EoR) are epochs of the Universe
which host invaluable information about the cosmology and astrophysics of X-ray
heating and hydrogen reionization. Radio interferometric observations of the
21-cm line at high redshifts have the potential to revolutionize our
understanding of the universe during this time. However, modeling the evolution
of these epochs is particularly challenging due to the complex interplay of
many physical processes. This makes it difficult to perform the conventional
statistical analysis using the likelihood-based Markov-Chain Monte Carlo (MCMC)
methods, which scales poorly with the dimensionality of the parameter space. In
this paper, we show how the Simulation-Based Inference (SBI) through Marginal
Neural Ratio Estimation (MNRE) provides a step towards evading these issues. We
use 21cmFAST to model the 21-cm power spectrum during CD-EoR with a
six-dimensional parameter space. With the expected thermal noise from the
Square Kilometre Array (SKA), we are able to accurately recover the posterior
distribution for the parameters of our model at a significantly lower
computational cost than the conventional likelihood-based methods. We further
show how the same training dataset can be utilized to investigate the
sensitivity of the model parameters over different redshifts. Our results
support that such efficient and scalable inference techniques enable us to
significantly extend the modeling complexity beyond what is currently
achievable with conventional MCMC methods.
