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I am trying to thoroughly understand the ROC Curve and I was wondering why is an ROC Curve always (seemingly) TPR against FPR? I have had discussions with others about this matter and I cannot think of any reasons why it could not be, for example, FPR against TPR. Thank you for your time!

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I think the reason is mainly conventional: If you plot FPR against TPR you obtain the same curve, except that is concave upward instead of downward, and the conventional summary statistics change meaning; e.g. the area under the curve (AUC) would decrease instead of increasing with classification accuracy.

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  • $\begingroup$ Yes, I think if you look into the history of the ROC it will also provide some insight. It was initially used to judge the performance of radar operators (how many real calls did they make versus false alarms?). $\endgroup$
    – Emma Jean
    Apr 8 '20 at 15:02
  • $\begingroup$ Thank you guys for your insights! I really appreciate it :) Also, @EmmaJean, may I know if you might know a good website to have a read about the history of ROC? Thank you again! :) $\endgroup$
    – leph
    Apr 9 '20 at 6:56

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