Editing Influence diagram (section)

==Applicability to value of information==

The above example highlights the power of the influence diagram in representing an extremely important concept in decision analysis known as the [[value of information]].  Consider the following three scenarios;
:*Scenario 1: The decision-maker could make their ''Vacation Activity'' decision while knowing what ''Weather Condition'' will be like.  This corresponds to adding extra informational arc from ''Weather Condition'' to ''Vacation Activity'' in the above influence diagram.
:*Scenario 2: The original influence diagram as shown above.
:*Scenario 3: The decision-maker makes their decision without even knowing the ''Weather Forecast''.  This corresponds to removing informational arc from ''Weather Forecast'' to ''Vacation Activity'' in the above influence diagram.

Scenario 1 is the best possible scenario for this decision situation since there is no longer any uncertainty on what they care about (''Weather Condition'') when making their decision.  Scenario 3, however, is the worst possible scenario for this decision situation since they need to make their decision without any hint (''Weather Forecast'') on what they care about (''Weather Condition'') will turn out to be.

The decision-maker is usually better off (definitely no worse off, on average) to move from scenario 3 to scenario 2 through the acquisition of new information.  The most they should be willing to pay for such move is called the [[value of information]] on ''Weather Forecast'', which is essentially the [[expected value of sample information|value of imperfect information]] on ''Weather Condition''.

The applicability of this simple ID and the value of information concept is tremendous, especially in [[Decision-making|medical decision making]] when most decisions have to be made with imperfect information about their patients, diseases, etc.