\bar{T}_{\rm b}(z) -1$, to be this statistic. It is important to note that while we restrict our default analysis to $\Delta^{2}_{21}(k,z)$, in principle any statistical measure of the cosmic 21 cm signal could be used in our framework.

The MCMC driver {#sec:MCMC}
---------------

An MCMC based [EoR]{} tool is a computationally challenging prospect since each step in the computation chain requires a [<span style="font-variant:small-caps;">21CMFAST</span>]{} realization. For reference, computing a 128$^{3}$ 21 cm realization at a single redshift takes $\sim3$s using a single core. This is efficient, however, it is a case of diminishing returns if we attempt to improve the computation time using the inbuilt multithreading of [<span style="font-variant:small-caps;">21CMFAST</span>]{}. Therefore, constructing an MCMC analysis tool which samples [<span style="font-variant:small-caps;">21CMFAST</span>]{} utilizing existing serial MCMC algorithms such as Metropolis–Hastings (@Metropolis:1953p2224 [@Hastings:1970p97]), which require multiple long computation chains, would be too computationally inefficient.

In recent years, several new, more efficient and parallel MCMC algorithms have been developed. Once such algorithm is the affine invariant ensemble sampler developed by @Goodman:2010p843. This algorithm has since been modified and improved before being released as the publicly available <span style="font-variant:small-caps;">python</span> module [<span style="font-variant:small-caps;">emcee</span>]{} by @ForemanMackey:2013p823. Recently, @Akeret:2012p842 discussed the virtues of adopting these computational algorithms for applications 