9781118041581

we conclude that Pr(LCƒS) 4Pr(LC). In words, the risk of lung cancer for a

smoker is fourtimes the overall risk of lung cancer (for smokers and non-

smokers together).

550 Chapter 13 The Value of Information

CHECK

STATION 2

The partners face the same seismic test as earlier and (as in Check Station 1) hold the

prior probability Pr(W) .28. Determine the optimal actions in light of the test, and

calculate the resulting expected profit. What is the value of the test?

VALUELESS INFORMATION Not all new information is of value to the deci-

sion maker. The key question in evaluating new information is: What impact

does it have in revising the decision maker’s initial probability assessment? Con-

sider again Bayes’ theorem (Equation 13.4) in the context of the oil-drilling

problem:

.

Suppose the test’s past track record is such that Pr(GƒW) Pr(G). In words,

this says the chance of getting a good test for sites containing oil is no

greater than the overall frequency of good tests at all sites, wet and dry.

Clearly, the test would appear to have little predictive value; its result is com-

pletely uncorrelated with the true condition of the site, wet or dry. Bayes’

theorem confirms that the test is valueless.Since the first factor in Equation

13.4 is 1, it follows that. The new probability is identical

to the prior probability; there is no probability revision. This being the case,

the partners’ decisions will not be affected by the outcome of the test.

Obviously, then, their expected profit also will be unchanged; that is, the

expected value of this new information will be zero. Such information is

valueless.

Pr(WƒG)Pr(W)

Pr(WƒG)c

Pr(GƒW)

Pr(G)

d Pr(W)

CHECK

STATION 3

The partners wish to evaluate the quality of a new seismic test before deciding to pay for

it. They assess the following joint probabilities: Pr(W&G) .32, Pr(B&D) .12,

Pr(B&W) .08, and Pr(G&D) .48. What is the value of the test?

There is one other important case in which new information or a test result

would have no value. This occurs when the decision maker’s optimal decision

is unaffected by the test result even though the outcome may cause him or her

to revise the probabilities. The decision maker takes the same actions with or

without the test and so earns the same expected profit in each instance. Again

the EVI is zero. Here’s an illustrative example.

A NEW SEISMIC TEST Suppose the quality of a new seismic test is summarized

in the table. What is the EVI of this test?

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