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4.3 Model-Free Techniques 117

event. A classification method with high sensitivity will rarely miss the
abnormal event when it occurs.
- True Negative Ratio = TNR = dl(c+d). Also known as spec$city, this parameter
tells us how specific our decision method is in the detection of the abnormal
event. A classification method with a high specificity will have a very low rate
of false alarms, caused by classifying a normal event as abnormal.
- False Positive Ratio = FPR = cl(c+d) = 1 - specificity.
- False Negative Ratio = FNR = bl(a+b) = 1 - sensitivity.

Both the sensitivity and specificity are usually given in percentages. A decision
method is considered good if it simultaneously has a high sensitivity (rarely misses
the abnormal event when it occurs) and a high specificity (has a low false alarm
rate).
The ROC curve depicts the sensitivity versus the FPR (complement of the
specificity). Let us illustrate the application of the ROC curve using the Signal
Noise dataset (see Appendix A). This set presents 100 signal+noise samples s(n)
consisting of random noise plus signal impulses with random amplitude, occurring
at random times according to the Poisson law. The signal+noise is shown in Figure
4.32.
The signal+noise amplitude is often greater than the average noise amplitude,
therefore revealing the presence of the signal impulses (e.g. at time instants 53 and
85). Imagine that we decide to discriminate between signal and noise simply by
using an amplitude threshold, A, such that we decide "impulse" (our abnormal
event) if s(n) >A, and "noise" (the normal event) otherwise. For a given threshold
value one can establish the signal vs. noise classification matrix and compute the
sensitivity and spccificity values. By varying the threshold (easily done in the
Signal Noise.xls file), the corresponding sensitivity and specificity values can then
be obtained, as shown Table 4.3.

I - - . I
Figure 4.32. One hundred samples of a signal consisting of noise plus signal
impulses (bold lines) occurring at random times.