Figure 7

Choice of help models. (A,B) A beneficial help model. Green circles correspond to bootstrap samples from a static example cloud. The red dot correspond to a measured data point example, that makes use of the tilting of the green cloud away from the axes. The shape of the green cloud and the distance to the red symbol is invariant when one transforms from the χ ² vs χ ² plane (A) to the LHR vs LHP plane (B). Importantly, the distance between the red symbol and the green cloud can be seen in the 1D projection to the LHR plane. (C-F) Illustration of how a bad, hyper-flexible, help-mode can be understood. (C) Model fit (blue dashed) to data (red vertical lines) for the hyper-flexible help-model. (D) same as in (A) but where the help-model is the hyper-flexible model. This cloud does not lie away from the axis, but parallel to the x-axis. Hence, all information is already contained within one dimension, and transforming to the LHR vs LHP plane will not help. (E) The 1D χ ² test (red) and the LHR (orange) empirical distributions for the case of a hyper-flexible model, each being the mirror image of the other. (F) A ROC analysis comparing a good help model with the bad hyper-flexible help-model in the static example. As before, 1D LHR (solid orange) is on top, above the 2D χ ² vs χ ² plot (solid purple) and the 1D χ ² (solid red). Those are the plots with the good help-model. The new plots with the bad hyper-flexible help-model lie below, and LHR becomes equally bad as the two-tailed χ ² test (the orange dashed and red dashed lines are superimposed). The 2D χ ² vs χ ² test (dashed purple) is slightly better, but still worse than the χ ² test.