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In decision theory, the expected value of perfect information (EVPI) is the price that one would be willing to pay in order to gain access to perfect information.〔Douglas Hubbard "How to Measure Anything: Finding the Value of Intangibles in Business" pg. 46, John Wiley & Sons, 2007〕 A common discipline that uses the EVPI concept is health economics. In that context and when looking at a decision of whether to adopt a new treatment technology, there is always some degree of uncertainty surrounding the decision, because there is always a chance that the decision turns out to be wrong. The expected value of perfect information analysis tries to measure the expected cost of that uncertainty, which “can be interpreted as the expected value of perfect information (EVPI), since perfect information can eliminate the possibility of making the wrong decision” at least from a theoretical perspective. == Equation == The problem is modeled with a payoff matrix ''Rij'' in which the row index ''i'' describes a choice that must be made by the payer, while the column index ''j'' describes a random variable that the payer does not yet have knowledge of, that has probability ''pj'' of being in state ''j''. If the payer is to choose ''i'' without knowing the value of ''j'', the best choice is the one that maximizes the expected monetary value: : where : is the expected payoff for action ''i'' i.e. the expectation value, and : is choosing the maximum of these expectations for all available actions. On the other hand, with perfect knowledge of ''j'', the player may choose a value of ''i'' that optimizes the expectation for that specific ''j''. Therefore, the expected value given perfect information is : where is the probability that the system is in state ''j'', and is the pay-off if one follows action ''i'' while the system is in state ''j''. Here indicates the best choice of action ''i'' for each state ''j''. The expected value of perfect information is the difference between these two quantities, : This difference describes, in expectation, how much larger a value the player can hope to obtain by knowing ''j'' and picking the best ''i'' for that ''j'', as compared to picking a value of ''i'' before ''j'' is known. Note: EV|PI is necessarily greater than or equal to EMV. That is, EVPI is always non-negative. EVPI provides a criterion by which to judge ordinary mortal forecasters. EVPI can be used to reject costly proposals: if one is offered knowledge for a price larger than EVPI, it would be better to refuse the offer. However, it is less helpful when deciding whether to accept a forecasting offer, because one needs to know the quality of the information one is acquiring. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「expected value of perfect information」の詳細全文を読む スポンサード リンク
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