## ROC curves in statistics.

A ROC curve or receiver operating characteristic curve, is a graphical plot that illustrates the diagnostic ability of a binary classifier system as its discrimination thresholds are varied. The ROC curve is created by plotting the true positive rate (TPR) against the false positive rate (FPR) at various threshold settings.

The top left corner of the plot is the “ideal” point - a false positive rate of zero, and a true positive rate of one. This is not very realistic, but it means that a larger area under the curve (AUC) is usually better.

Also:

Smaller values on the x-axis of the plot indicate lower false positives and higher true negatives.

Larger values on the y-axis of the plot indicate higher true positives and lower false negatives.

## Generating data and drawing ROC curves:

```
import numpy as np
import matplotlib.pyplot as plt
import scipy.stats as stats
## generating d-prime and response bias
x = np.arange(.01,1,.01)
dp = np.tile(stats.norm.ppf(x),(99,1)).T - np.tile(stats.norm.ppf(x),(99,1))
rb = -( np.tile(stats.norm.ppf(x),(99,1)).T + np.tile(stats.norm.ppf(x),(99,1)) )/2
## create the 2D bias spaces and plot their ROC curves
rb2plot = [.3, .5, .9, 1.5] # d'/bias levels
tol = .01 # tolerance for matching levels
colorz = 'rbmk'
# setup the figure
fig,ax = plt.subplots(1,2,figsize=(10,5))
# show the 2D spaces
ax[0].imshow(dp,extent=[x[0],x[-1],x[0],x[-1]],origin='lower')
ax[0].set_xlabel('False alarm rate')
ax[0].set_ylabel('Hit rate')
ax[0].set_title("d'")
ax[1].imshow(rb,extent=[x[0],x[-1],x[0],x[-1]],origin='lower')
ax[1].set_xlabel('False alarm rate')
ax[1].set_ylabel('Hit rate')
ax[1].set_title('Response bias')
### now draw the isocontours
for i in range(len(rb2plot)):
# find d' points
idx = np.where((dp>rb2plot[i]-tol) & (dp<=rb2plot[i]+tol))
ax[0].plot(x[idx[1]],x[idx[0]],'o-',color=colorz[i])
# find bias points
idx = np.where((rb>rb2plot[i]-tol) & (rb<=rb2plot[i]+tol))
ax[1].plot(x[idx[1]],x[idx[0]],'o-',color=colorz[i])
plt.show()
```