Permutation tests with a simulated data set with *A*=7.5%. *a,* The permutation surface. The height of the surface at point (*i*,*p*_{i}) is the marker frequency of marker *m*_{i} that has an estimated markerwise *P* value of *p*_{i}. The observed frequency is plotted on the surface by projecting it from the marker-frequency plane onto the permutation surface. The closer the line gets to the ‘back wall’, the more significant is the marker frequency. *b,* Marker frequencies for different *P* values. The solid line shows the observed marker frequencies in the simulated data; the dashed lines have been plotted by connecting marker frequencies for which the markerwise *P* values are the same. *c,* Marker frequencies for different *P* values in an unsuccessful localization. The solid line shows the observed marker frequencies in the simulated data; the dashed lines have been plotted by connecting marker frequencies for which the markerwise *P* values are the same. *d,* The effect of permutation tests on prediction accuracy, with 100 data sets where *A*=5%. The solid line represents localization accuracy without permutations, and the dashed lines show the prediction accuracy with the smallest marker-wise *P* value (“min p”), or with the smallest *P* value at most .01 or .001. If the smallest *P* value is >.01 or .001, no prediction is made at all; the fraction on *y* axis is computed among the predictions made. The lowest, dotted curve is the prediction accuracy of random, uniform guesses.

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