One-dimensional posterior distributions for cosmological and nuisance parameters using TT+SimAll. The black line shows the baseline set of results, which adopts priors on the dust amplitudes. The red lines show the case when we leave the amplitudes free to vary; these are in good agreement with the priors set in the baseline, which are indicated with grey dotted lines. As a consequence, leaving the dust amplitudes free to vary without priors has small to negligible impact on other parameters.