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That's a lot of text to get to ROC curves...I'd rewrite down to essentials and get to the curves ASAP.

Fundamentally, you have a threshold. Things above are classified as "positive" and below as "negative". At different threshold values, you get some number of correct positives (was actually positive) and false positives (was actually negative). That's what the ROC curve shows. You want the curve to be as close to the top-left (in this case) corner as possible.

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replace threshold with parameter,

classifiers may have different parameters other than threshold

Area under ROC curves (AUC) are used to evaluate how good the model is considering many parameters can be chosen for it.

However, when you actually want to make a prediction, you still need to pick a value for the parameter (a point on the ROC curve). So F-measure is often more useful for evaluating the predictions. While AUC are more useful at evaluating classifiers.

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