Page 137 - Introduction to Statistical Pattern Recognition

3 Hypothesis Testing 119

lo4 as and &2 by observing an average of 27.6 samples. This indicates how
errors can be significantly reduced by using a relatively small number of obser-
vations.

Computer Projects

Two normal distributions are specified by the following parameters.

1. Generate 100 samples from each class.
2. Design the Bayes classifier for minimum error by using given Mi, Xi and
Pi (the theoretical classifier). Classify the generated samples by the
classifier, and count the number of misclassified samples.
3. Plot the theoretical distribution function derived from (3.73) and the
empirical distribution functions of (3.71), and test the normality of the
generated samples.
4. Plot the operating characteristics by classifying the generated samples
with the theoretical classifier.
5. Plot the error-reject curve by classifying the generated samples with the
theoretical classifier.
6. Compute the theoretical Bayes error for the given normal distributions.
7. Changing the threshold value t in Project 6, plot the theoretical operating
characteristics and error-reject curve, and compare them with the results
of Projects 4 and 5.
8. Plot the Chemoff bound as a function of s, and find the optimum s and
the minimum Chemoff bound.
9. Perform the sequential classification for m =9 and 25. Generate 100 m-
sample-groups-from each class and count the number of misclassified
rn-sample-groups.