5
5
5
io
io
37
I2Ö
c-3 0i, «2 (there is a gross error, no remeasurement)
a. Loss of time in the office. The computer first
checks his own work, and then comes to the
surveyor to ask if anything can be wrong. hour
b. The surveyor talks him out of his doubts, but
afterwards he feels uneasy himself
c. A measurement in the same area next year shows
discrepancies. Loss of time
d. Same thing the year after
e. Finally someone decides to remeasure the
distance
f. Loss of prestige for the surveyor
1(01,«2)
c-4 02, «2 (no gross error, no measurement)
^(02, dl)
Summarizing we get the following table of losses of utility.
«1
a2
0i
20
37
02
25
o
TABLE i.
Losses of utility
d. The observation variate t.
We simplify the problem by distinguishing only the following
possible observations (unitcm)
fa o t 8
fa 8 t j 12
fa 12 t
t is always normally distributed with standard deviation at 4 cm.
Denote the mean by t.
If 0i is the state of nature, t io cm.
If 02 is the state of nature, t o cm.
e. The strategies s.
A strategy is a decision rule which assigns an action to each
possible observation of the observation variate. One strategy is,
e.g. always to remeasure, whatever value t is observed. Another
one would be to remeasure when fa is observed and not to remeasure
when fa or fa is observed. Since there are three possible observations
and two available actions, there are 23 8 possible strategies,
which are listed below in table 2.
2
