are made as above resulting in:
4
Pfa: 01 ˆy, 1 0.845@@
4
Pfa: 11 ˆy, 0.845 10@@
Again it is seen that the failure probabilities are reduced as an effect of the observed yield
strength. On the basis of the new information and the resulting posterior probabilistic models
the decision problem considering whether or not a strengthening of the steel bar is cost
effective may be revisited as shown in Figure 12.8.
Figure 12.8: Simple decision problem with expected costs.
By comparison of Figure 12.8 and Figure 12.6 it is seen that the cost optimal decision on the
basis of the test result has shifted from strengthening the steel bar, to not strengthening the
steel bar. The test result has reduced the uncertainty of the steel yield stress so much that it is
no longer cost effective to perform a strengthening.
It should be noted that the calculations of the posterior probabilistic models could have been
performed in more straightforward ways. The approach followed in the above, however,
highlights the Bayesian thinking in decision analysis and is readily applied also in problems
where the uncertainties have discrete probability distribution functions.
Updating of prior probabilistic models may be performed in a number of ways. Which
approach is the most appropriate depends on the type of information and not least the applied
prior probabilistic modelling in the individual cases. In the following some general
approaches are given on how posterior probabilistic models can be established.
Decision analysis concerning collection of information
Often the decision-maker has the option to ‘buy’ additional information through an
experiment before actually making his choice of action. If the cost of this information is small
in comparison to the information on the state of nature it promises the decision-maker should
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