From the action probabilities and the loss table, the expected
losses £(0,s) are now derived. For example, £(0r, si) is the expected
loss if 0i is the state of nature and the strategy Si is chosen. Strategy
Si always takes ai (probability 1), hence
£(0i, si) 1 X 20 o X 37 20
£(02, si) 1 X 25 o X o 25.
In the same way one finds, e.g.
The results for all strategies are given in table 5.
4. Selecting a Strategy
From the expected losses in table 5 it cannot easily be judged
what would be a good strategy. It is very helpful to draw a diagram
in an orthogonal coordinate system we can plot each strategy as
a point, having £(0i, s) and £(62,s) for coordinates, see fig. 2. If we
now look at S3, we see that it has high expected losses, whatever
the state of nature is. We recall that S3 is the strategy taking «1
when t\ is observed, «2 when fa or fa is observed. This means that
adopting S3 will result in remeasurement when the difference
between direct and reverse measurements is small, whereas large
differences are accepted without remeasurement. Under a different
model for the possible states of nature such a strategy might be
useful, e.g. if one suspects the chainmen of cheating when the
results look too good to be true. But in the present situation it is a
129
*7
ai
a-2 s8
ai
«2
A,
0
I 0!
0.3085
0.6915
02
0
I 02
0.0027
0.9973
Loss table
ai
a-2
01
20
37
02
25
0
TABLE 4.
Action probabilities
£(0i, s4) 0.6170 X 20 0.3820 X 37 26.51
£(02, s4) 0.9572 X 25 0.0428 X o 23.93.
Si
s2
S3
«4
*5
S6
*7
S8
0i
20
25.24
31-76
26.51
25.24
30-49
37
31-76
02
25
24-93
23.86
23-93
1.14
I.O7
0
0.07
TABLE 5.
Expected losses
