Regularized emission measure distributions (black solid line and grey error bars) for the active region core observations made by Warren et al. (2010), their MCMC solution (red histogram) is shown for comparison. In the right-hand panels the positivity constraint was used and hence larger χ² values are achieved by the regularized solutions. The EM loci curves for the Hinode/EIS (coloured lines) and Hinode/XRT filter (black dashed line) are shown in the bottom left panel and their minimum was used as an initial guess solution for the regularizations shown in the bottom row.