Figure 1:
Figure 1: Histogram of the maximum Likelihood distribution for the 1000 simulations of model 00, in the case where we only impose flat priors to the parameters, with no decorrelation in the model. Bottom plot is a zoomed in version.
The dashed grey line representes the number of degrees of freedom, for 9 frequencies (9*10/2 cross spectra), 9 bandpowers, with 10 free parameters in the model: 405-10 dof. Here we are plotting the -2 log(likelihood) as it comes out of minuit. Since we used the HL likelihood, we don't expect it to exactly be a \(\chi^2\) distribution, but for model 00, it seems like it still peaks at the number of degrees of freedom.
Figure 2:
Figure 2: Same as figure 1, but for the case where we include decorrelation in the model. Note that we now have a good fit to model 5.