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The effect of new information 223
Posterior probability of gas being found
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
95% reliable
70% reliable
50% reliable
Prior probabilities are unchanged
10% reliable
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Prior probability of gas being found
Figure 8.6 – The effect of the reliability of new information on the modification of prior
probabilities for the gas-exploration problem
be seen in Figure 8.6. In the figure the horizontal axis shows the prior
probability that gas will be found, while the vertical axis represents the
posterior probability when the test drilling has indicated that gas will be
found. For example, if the prior probability is 0.4 and the result of the test
drilling is 70% reliable then the posterior probability will be about 0.61.
The graph shows that if the test drilling has only a 50% probability
of giving a correct result then its result will not be of any interest and
the posterior probability will equal the prior, as shown by the diagonal
line on the graph. By considering the distance of the curves from the
diagonal line, it can be seen that the more reliable the new information,
the greater will be the modification of the prior probabilities. For any
given level of reliability, however, this modification is relatively small
either where the prior probability is high, implying that the geologist
has a strong belief that gas will be found and the test drilling confirms