The power spectrum of redshifted 21 cm emission brightness temperature fluctuations is a powerful probe of the Epoch of Reionization (EoR). However, bright foreground emission presents a significant impediment to its unbiased recovery from interferometric data. We build on the Bayesian power spectral estimation methodology introduced in Sims et al. 2016 and demonstrate that incorporating a priori knowledge of the spectral structure of foregrounds in the large spectral scale component of the data model enables significantly improved modelling of the foregrounds without increasing the model complexity. We explore two astrophysically motivated parametrisations of the large spectral scale model: (i) a constant plus power law model of the form $q_{0}+q_{1}( u/ u_{0})^{b_{1}}$ for two values of $b_{1}$: $b_{1} = <beta>_mathrm{GDSE}$ and $b_{1} = <beta>_mathrm{EGS}$, the mean spectral indices of the Galactic diffuse synchrotron emission and extragalactic source foreground emission, respectively, and (ii) a constant plus double power law model of the form $q_{0}+q_{1}( u/ u_{0})^{b_{1}}+q_{2}( u/ u_{0})^{b_{2}}$ with $b_{1} = <beta>_mathrm{GDSE}$ and $b_{2} = <beta>_mathrm{EGS}$. We estimate the EoR power spectrum from simulated interferometric data consisting of an EoR signal, Galactic diffuse synchrotron emission, extragalactic sources and diffuse free-free emission from the Galaxy. We show that, by jointly estimating a model of the EoR signal with the constant plus double power law parametrisation of the large spectral scale model, unbiased estimates of the EoR power spectrum are recoverable on all spatial scales accessible in the data set, including on the large spatial scales that were found to be contaminated in earlier work.
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