Summary statistics of the reconstructed power spectra from the inferred posterior initial density field realisations depicted in Fig. 8, with the ensemble mean indicated by a solid green line. The solid blue line corresponds to the ensemble mean of the power spectra realisations generated using the inferred cosmological parameters. The shaded regions indicate their respective 1σ confidence region, i.e. 68% probability volume. This plot shows that the prior information entropy is inferior to the posterior information entropy, due to the narrower distribution of the former. The prior power spectrum adopted, as a result, does not impact significantly on the cosmological parameter inference via the AP test.