Titel_SS06

  >?

>?

>?

| 313 min [ | ] (100 10) [ 23 | ] 10; 100

min 0.75 (100 10) 0.25 10;100

min 85;100 85

@@  @@ @@

 



ECI P I P I

MU

::

where the posterior probabilities P'':i I 1 and P'':iI 2 are determined as already shown

in Section 3.7 forP'':i I 3.

The expected cost corresponding to the situation where the experiment with the experiment
costs CP is therefore:

   |[] 11   | []2 2  |[3 3

(25.8 ) 0.38 (100 ) 0.46 (85 ) 0.16

(69.4 )

 @@ @ @@ @ @@ @

   



PP

P

EC ECIPI ECI PI ECI PI

CCC

CMU

]

P^

By comparison of this result with the expected cost corresponding to the prior information it
is seen that the experiment should be performed if the costs of the experiment is less than 0.6:

EC EC@   70 (69.4 CP) 0.6 CP

3.9 The Risk Treatment Decision Problem

Having introduced the fundamental concepts of decision theory it will now be considered how
these carry over to the principally different types of risk analysis.

The simplest form of the risk analysis, i.e. a simple evaluation of the risks associated with a
given activity and/or decision alternative may be related directly to the prior decision analysis.
In the prior analysis the risk is evaluated on the basis of statistical information and
probabilistic modelling available prior to any decision and/or activity. A simple
decision/event tree in Figure 3.6 illustrates the prior analysis. In a prior analysis the risk for
each possible activity/option may e.g. be evaluated as:



1

n

ii

i

R EU PC



 (3.9)

where R is the risk, U the utility, is the ith branching probability and the consequence

of the event of branch i.

Pi Ci

A prior analysis in fact corresponds closely to the assessment of the risk associated with a
known activity. A prior analysis thus forms the basis for the comparison of risks between
different activities.