From a set of 8 \(1024^3\) simulations where the parameters are:

\(\beta_{\mathrm{He}} = [0.3 \,\,\,\, 0.9 ]\) \(\beta_{\mathrm{H}} = [0.6 \,\,\,\, 1.0 ]\) \(\Delta z_{\mathrm{He}} = [0.0 \,\,\,\, 0.8 ]\)

First I fit each redshift independently:

The 95% Highest Probability Interval from the posterior distribution of the fitted parameters ( as a function of redshift, since each redshift is fitted independently ) is shown below, there are no constrains for the Helium parameters:

Now I fit all the redshifts simultaneously:

And the posterior distribution of the parameters are:

Resulting in a delayed Helium reionization but with High photoheating and photoinization rates.