Page 138 - Introduction to Statistical Pattern Recognition

120 Introduction to Statistical Pattern Recognition

Problems

1. Two one-dimensional distributions are uniform in [0, 21 for 01 and [ 1, 41
for q, and PI = P2 = 0.5.

(a) Find the Bayes boundary for minimum error, and compute the
Bayes error.
(b) Plot the operating characteristics.
(c) Find the Neyrnan-Pearson boundary with = 0.25.
(d) Find the minimax boundary.

(e) Compute the Chernoff bound, and find the optimal s.
(f) Compute the Bhattacharyya bound.
2. Two normal distributions are characterized by
Pi =P2 =0.5,

(a) Draw the Bayes decision boundary to minimize the probability of
error.

(b) Draw the Bayes decision boundary to minimize the cost with
cII =~~~=Oandc~~=2c~,.
3. Repeat Problem 2 for

4. Assuming that c II = c22 = 0 and c 12 =c21 in Problem 2, plot the rela-
tionship between the threshold values of the likelihood ratio and the pro-
babilities of errors.
(a) Plot the operating characteristics.
(b) Find the total error when the Neyman-Pearson test is performed
with E] = 0.05.
(c) Find the threshold value and the total error for the minimax test.