In Arxiv: 1511:xxxx we run a chain to the forecasted Euclid Cluster Counts Chain (Download the chain) using the MathMC. All the started points were points of high likelihood so that you don’t need to worry about any burn-in phase. The results from Gelman-Rubin test for all variables are lower than 0.02 and the plots for the power spectrum of the chain are:

Both results presents the expected feature for a slightly converged chain (see more information about chain convergence in Verde et. al) which are good enough for the the paper proposal.