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92 4 Statistical Classification

Figure 4.12. Histograms of feature N for two classes of cork stoppers. The
threshold value N=65 is marked with a vertical line.

From this graphic display we can estimate the likelihoods3:

We then decide class q, although the likelihood of w I is bigger than that of y.
Notice how the statistical model changed the conclusions derived by the minimum
distance classification (see 4.1.3).
Figure 4.13 illustrates the effect of adjusting the prevalence threshold assuming
equal and normal pdfs:

Equal prevalences. With equal pdfs, the decision threshold is at half distance
from the means. The number of cases incorrectly classified, proportional to the
shaded areas, is equal for both classes. This situation is identical to the
minimum distance classifier.
Prevalence of wl bigger than that of a. The decision threshold is displaced
towards the class with smaller prevalence, therefore decreasing the number of
cases of the class with higher prevalence that are wrongly classified, as it seems
convenient.

1
The normal curve fitted by Statistics is multiplied by the factor (number of
cases)x(histogram interval width), which is 100 in the present case. This constant factor is
of no importance and is neglected in the computations (4-16).