
52 Statistical Computing in Nuclear Imaging
in Table 2.5) the decision in favor of hypothesis 1 should be made when the
second roll g is 1, 2, or 3, and in favor of hypothesis 2 when the second roll is
4, 5, or 6.
TABLE 2.5
Values of posterior expected losses for composite hypotheses
p(Θ
1
|G = g) p(Θ
2
|G = g) ̺(δ(H
1
); G = g) ̺(δ(H
2
); G = g)
g ↓ 1 125/147 22/147 22x/147 125x/147
2 65/87 22/87 22x/87 65x/87
3 35/57 22/57 22x/57 35x/57
4 15/37 22/37 22x/37 15x/37
5 0 1 x 0
6 0 1 x 0
2.3.4 BINARY HYPOTHESIS TESTING/DETECTION
The previous section discussed the general multiple-alternative decision mak-
ing that includes binary hypothesis testing. We dedicate here ...