We present a Markov Chain Monte Carlo (MCMC)-based parameter estimation package, CosmoReionMC, to jointly constrain cosmological parameters of the $Lambda$CDM model and the astrophysical parameters related to hydrogen reionization. The package is based on a previously developed physically motivated semi-analytical model for reionization, a similar semi-analytical model for computing the global 21~cm signal during the cosmic dawn and using an appropriately modified version of the publicly available CAMB for computing the CMB anisotropies. These calculations are then coupled to an MCMC ensemble sampler texttt{emcee} to compute the posterior distributions of the model parameter. The model has twelve free parameters in total: five cosmological and seven related to the stellar populations. We constrain the parameters by matching the theoretical predictions with CMB data from Planck, observations related to the quasar absorption spectra and, for the first time, the global 21~cm signal from EDGES. We find that incorporating the quasar spectra data in the analysis tightens the bounds on the electron scattering optical depth $tau$ and consequently the normalization $A_s$ of the primordial matter power spectrum (or equivalently $sigma_8$). Furthermore, when we include the EDGES data in the analysis, we find that an early population of metal-free stars with efficient radio emission is necessary to match the absorption amplitude. The CosmoReionMC package should have interesting future applications, e.g., probing non-standard extensions to the $Lambda$CDM model.
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