3.5 Decision Making Subject to Uncertainty
Having formulated the decision problem in terms of a decision/event tree, with proper
assignment of utility and probability structure, the numerical evaluation of decision
alternatives may be performed.
Depending on the state of information at the time of the decision analysis, three different
analysis types are distinguished, namely prior analysis, posterior analysis and pre-posterior
analysis. All of these are important in practical applications of decision analysis and are
therefore discussed briefly in the following.
3.6 Decision Analysis with Given Information - Prior Analysis
When the utility function has been defined and the probabilities of the various states of nature
corresponding to different consequences have been estimated, the analysis reduces to the
calculation of the expected utilities corresponding to the different action alternatives. In the
following the utility is represented in a simplified manner through the costs, whereby the
optimal decisions now should be identified as the decisions minimizing expected costs, which
then is equivalent to maximizing expected utility.
At this stage the probabilistic description [ ]P: of the state of nature : is usually called a
prior description and denoted '[ ]P :.
To illustrate the prior decision analysis the decision problem from Section 2.2 is considered
again. The decision problem is stated as follows. The decision maker has a choice between
two actions:
a 1 : Establish a new well.
a 2 : Establish a pipeline from an existing well.
The possible states of nature are the following two:
: 1 : Capacity insufficient.
: 2 : Capacity sufficient.
The prior probabilities are:
'[ ]P :< = 0.60
'[ ]P := = 0.40
Based on the prior information alone it is easily seen that the expected cost E'C amounts
to:
E@@CP min> :: 12 (100 10) P@ 10; 100? min 70;100>? 70 MU.