Mismatch between the data and the result of a sampler that includes the input correlations between the components during the sampling process (top) and its PDF (bottom). In the upper panel the red line represents the mean of the expected chi-squared distribution that D_ℓ should follow. In the bottom panel, the blue lines are the best χ²-fit to a chi-squared curve and the ± 1 standard deviation error from the fit. The red dashed line represents the chi-squared distribution with the expected number of degrees of freedom N_d.o.f. = 7. The introduction of the correlation between the input component erases the large discrepancy at low multipole.