Illustration of the reconstruction of the logarithmic power spectrum τ. Both panels show the default power spectrum (black dashed line), and the simulated realization (black dotted line), as well as the reconstructed power spectra using a MAP (orange solid line), plus second order corrections (orange dashed line), and a Gibbs approach (blue solid line). Panel a) shows the reconstruction for a chosen σ parameter of 10, panel b) for a σ of 1000.