P(k) MCMC Fit to Boss and Walther Data

From a set of 256 $1024^3$ simulations where the parameters are:

$$\beta_{\mathrm{He}} = [ 0.3, \, 0.53, \, 0.76, \, 1.0 ]$$ $$\beta_{\mathrm{H}} = [ 0.6, \, 0.73, \, 0.86, \, 1.0 ]$$ $$\Delta z_{\mathrm{He}} = [-0.1, \, 0.2, \, 0.5, \, 0.8 ]$$ $$\Delta z_{\mathrm{H}} = [ -0.6, \, -0.4, \, -0.2, \, 0.0 ]$$

I fit to the temperature data and the power spectrum from different data sets.

The distributions from fitting to the Boss and Walther data separately are:

When I fit to bot datasets simultaneously the results are very different:

Below is the evolution of the temperature from the fitted posterior distribution of the parameters:

Below is the evolution of the power spectrum from the fitted posterior distribution of the parameters:

Now fitting to Walther, Boera and Viel data sets: