the *a priori* assumptions on the intrinsic probability distribution (i.e. Gaussian). Moreover, by sampling over 10$^{5}$ realizations within [<span style="font-variant:small-caps;">21CMMC</span>]{} this allows us to sample many features within the [EoR]{} parameter space not visible in course-grid models. Additionally, this allows for the better characterization of parameter degeneracies, which is a problem for Fisher Matrix analyses.

Single Ionizing Galaxy Population {#sec:SGP}
=================================

To illustrate the use of [<span style="font-variant:small-caps;">21CMMC</span>]{}, we first adopt the popular three-parameter EoR model, discussed above. This model is characterized by a single population of efficient star-forming galaxies hosted by haloes above our defined critical temperature $T^{\rm Feed}_{\rm vir}$. The ionizing efficiency of this model is a step function, $$\begin{aligned}
 \label{eq:zeta_0}
\zeta(T_{\rm vir}) = \left\{ \begin{array}{cl} 
      \zeta_{0}  & {T_{\rm vir} \geq T^{\rm Feed}_{\rm vir}}\\
      0 & {T_{\rm vir} < T^{\rm Feed}_{\rm vir}}.
\end{array} \right.\end{aligned}$$ In this model, a constant fraction of the host halo mass goes into the production of ionizing photons. To illustrate the performance of [<span style="font-variant:small-caps;">21CMMC</span>]{}, we choose $\zeta_{0} = 30$, $R_{\rm mfp} = 15$ Mpc and $T^{\rm Feed}_{\rm vir} = 3\times10^{4}$ K for our mock observation. Our chosen values are roughly consistent with observational data, though they merely serve for illustrative purposes.

Building physical 