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566 CHAPTER 13 DECISION ANALYSIS

EVSI
E ¼ 100 (13:14)
EVPI

For the PDC problem,
1:73
E ¼ 100 ¼ 54:1%
3:2
In other words, the information from the market research study is 54.1 per cent as
efficient as perfect information.
Low efficiency ratings for sample information might lead the decision maker to
look for other types of information. However, high efficiency ratings indicate that
the sample information is almost as good as perfect information and that additional
sources of information would not yield significantly better results.

13.6 Calculating Branch Probabilities

In Section 13.5 the branch probabilities for the PDC decision tree chance nodes
were specified in the problem description. In this section we show how Bayes’
theorem can be used to calculate branch probabilities for decision trees.
The PDC decision tree is shown again in Figure 13.13. Let:

F ¼ Favourable market research report
U ¼ Unfavourable market research report
s 1 ¼ Strong demand (state of nature 1)
s 2 ¼ Weak demand (state of nature 2)
At chance node 2, we need to know the branch probabilities P(F) and P(U). At
chance nodes 6, 7 and 8, we need to know the branch probabilities P(s 1 |F) – the
probability of s 1 given that F has occurred – the probability of state of nature 1 given
a favourable market research report, and P(s 2 |F), the probability of state of nature 2
given a favourable market research report. P(s 1 |F) and P(s 2 |F) are referred to as
posterior probabilities because they are conditional probabilities based on the out-
come of the sample information. At chance nodes 9, 10 and 11, we need to know the
branch probabilities P(s 1 |U) and P(s 2 |U); note that these are also posterior prob-
abilities, denoting the probabilities of the two states of nature given that the market
research report is unfavourable. Finally, at chance nodes 12, 13 and 14, we need the
probabilities for the states of nature, P(s 1 ) and P(s 2 ), if the market research study is
not undertaken.
In making the probability calculations, we need to know PDC’s assessment of the
probabilities for the two states of nature, P(s 1 ) and P(s 2 ), which are the prior
probabilities as discussed earlier. In addition, we must know the conditional prob-
ability of the market research outcomes (the sample information) given each state of
nature. For example, we need to know the conditional probability of a favourable
market research report given that the state of nature is strong demand for the PDC
project; note that this conditional probability of F given state of nature s 1 is written
P(F|s 1 ). To carry out the probability calculations, we will need conditional proba-
bilities for all sample outcomes given all states of nature, that is, P(F|s 1 ), P(F|s 2 ),
P(U|s 1 ) and P(U|s 2 ). In the PDC problem, we assume that the following assess-
ments are available for these conditional probabilities.

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