2D parameter estimation of T₀ and Γ_HI using IMNN. Top: IMNN training plot (using SimulatorIMNN subclass of IMNN) corresponding to thermal parameter, T₀, and H I photoionization rate, Γ_HI, for z = 3. The plot shows the evolution of Fisher information during training with the training epoch. Bottom: Contour plots showing the 68% credible region for log T₀ and logΓ_HI/Γ_HI, Fid estimates based on the IMNN approach and with MCMC. It is to be noted that in the case of MCMC, the contour plot corresponds to a posterior distribution drawn from running MCMC using a flat prior (see Eq. 4), while in the case of IMNN it corresponds to the distribution of the estimates. Accompanying this are the plots for the distribution functions (for MCMC and IMNN, respectively) for both the parameters log T₀ and logΓ_HI/Γ_HI, Fid individually by marginalizing over the other parameters.