# ROC Curve

- Author:
- Victor Hui

- Topic:
- Statistics

## Receiver Operating Characteristic Curve

Correspondence between score distributions and the ROC curve
(https://en.wikipedia.org/wiki/Receiver_operating_characteristic)

- d (x-axis) is the score returned by a binary classifier
- The red and blue hatchings are distributions of the scores of the positive and negative truths
- Let the distributions be normal, move "
**<-->**" to adjust the location and scale - d* is a threshold setting to separate the mixing of the positive and negative classifications
- The blue shaded region (d < d*) is the distribution of false positive (FP) scores
- The red shaded region (d > d*) is the distribution of false negative (FN) scores
- The area of the blue shaded region yields the false positive rate FPR
- The area of the red hatching less the area of the red shade yields the truth positive rate TPR
- The ROC curve is the plot of TPR vs FPR as function of the threshold setting d*
- Move d* on Graph to trace the ROC curve on Graph2

*Question*:*Find an optimal threshold setting*d*