Prior
PosteriorLikelihoodLikelihood
PriorPosteriorPriorPosteriorLikelihoodFigure 3.4: Illustration of updating of probability structures.
In Figure 3.4 an illustration is given of corresponding prior and posterior probability density
functions together with likelihood functions. In the first case the prior information is strong
and the likelihood is weak (small sample size). In the second case the prior information and
the likelihood are of comparable strength. In the last case the prior information is relatively
weak in comparison to the likelihood.
To illustrate the posterior decision analysis the water supply decision problem is considered
again.
It is assumed that information about the capacity of the local reservoir can be estimated by the
implementation of a less expensive test well and subsequent pump test. It is assumed that the
cost of establishing a test well is equal to 1 monetary unit. However, the information obtained
from the pump test is only indicative as the result of the difference in scale from the test well
to the planned local well.
It is assumed that the pump test can provide the following different information – i.e.
indicators regarding the capacity of the local reservoir.
The capacity of the reservoir is:
larger than the given production requirements by 5% i.e. larger than 105 water volume
units per day,
less than 95% of the required water production, i.e. less than 95 water volume units,
between 95 and 105 water units.
The information from the pump test is subject to uncertainty and the likelihood of the actual
capacity of the local reservoir given the three different indications described above are given
in Table 3.1.