Page 126 - DMTH404_STATISTICS

Statistics

Notes The weighted average of these payoffs with weights equal to the probabilities of respective
states of nature is termed as Expected Payoff under Certainty (EPC).

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Thus, EPC = 200 0.3 200 0.4 600 0.3 = 320
The difference between EPC and EMV of optimal action is the amount of profit foregone due to
uncertainty and is equal to EVPI.
Thus, EVPI = EPC – EMV of optimal action = 320 – 194 = 126
It is interesting to note that EVPI is also equal to EOL of the optimal action.
8.1.1 Cost of Uncertainty

This concept is similar to the concept of EVPI. Cost of uncertainty is the difference between the
EOL of optimal action and the EOL under perfect information.

Given the perfect information, the decision maker would select an action with minimum
opportunity loss under each state of nature. Since minimum opportunity loss under each state of
nature is zero, therefore,
EOL under certainty 0 0.3 0 0.4 0 0.3= ´ + ´ + ´ = 0 .
Thus, the cost of uncertainty = EOL of optimal action = EVPI

Example 19: A group of students raise money each year by selling souvenirs outside the
stadium of a cricket match between teams A and B. They can buy any of three different types of
souvenirs from a supplier. Their sales are mostly dependent on which team wins the match. A
conditional payoff (in Rs.) table is as under :

Type Souvenir ® I II III
of
Team wins 1200 800 300
A
Team wins 250 700 1100
B
(i) Construct the opportunity loss table.
(ii) Which type of souvenir should the students buy if the probability of team A's winning is
0.6?
(iii) Compute the cost of uncertainty.
Solution.

(i) The Opportunity Loss Table

Actions ® Type Souvenir bought
of
II
I
Events ¯ III
Team wins 0 400 900
A
Team wins 850 400 0
B
(ii) EOL of buying type I Souvenir = 0 0.6 850 0.4 = 340
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EOL of buying type II Souvenir = 400 0.6 400 0.4 = 400.
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EOL of buying type III Souvenir = 900 0.6 0 0.4 = 540.
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