Expected value of perfect information


Expected value of perfect information

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]

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:: mbox{EMV} = max_i sum_j p_j R_{ij}. , where: sum_j p_j R_{ij}. , is the expected payoff for action "i" i.e. the expectation value, and: mbox{EMV} = max_i ,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: mbox{EV}|mbox{PI} = sum_j p_j (max_i R_{ij}), , where p_j is the probability that the system is in state "j", and R_{ij} is the pay-off if one follows action "i" while the system is in state "j".Here (max_i R_{ij}), , indicates the best choice of action "i" for each state "j".

The expected value of perfect information is the difference between these two quantities,: mbox{EVPI} = mbox{EV}|mbox{PI} - mbox{EMV}. , 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.

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.

References

ee also

*Expected value of sample information


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Expected value of perfect information — The expected value if the future uncertain outcomes could be known minus the expected value with no additional information. The New York Times Financial Glossary …   Financial and business terms

  • expected value of perfect information — The expected value if the future uncertain outcomes could be known minus the expected value with no additional information. Bloomberg Financial Dictionary …   Financial and business terms

  • Expected value of sample information — In decision theory, the expected value of sample information (EVSI) is the price that one would be willing to pay in order to gain access to a sample from the distribution about which the prediction has to be made. For example, if one needs to… …   Wikipedia

  • Value of information — (VoI) in decision analysis is the amount a decision maker would be willing to pay for information prior to making a decision. imilar termsVoI is sometimes distinguished into value of perfect information, also called value of clairvoyance (VoC),… …   Wikipedia

  • Information gain in decision trees — In information theory and machine learning, information gain is an alternative synonym for Kullback–Leibler divergence . In particular, the information gain about a random variable X obtained from an observation that a random variable A takes the …   Wikipedia

  • Information theory — Not to be confused with Information science. Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental… …   Wikipedia

  • Information Processing and Information Systems — ▪ 1995       Sweeping change marked the U.S. computer industry in 1994 as longtime players exited the stage and rival systems struggled to dominate the next generation of personal computer (PC) operating systems and microprocessors. The industry… …   Universalium

  • Perfect Dark — This article is about the Nintendo 64 video game. For other uses, see Perfect Dark (disambiguation). Perfect Dark …   Wikipedia

  • information theory — the mathematical theory concerned with the content, transmission, storage, and retrieval of information, usually in the form of messages or data, and esp. by means of computers. [1945 50] * * * ▪ mathematics Introduction       a mathematical… …   Universalium

  • Applied information economics — (AIE) is a decision analysis method developed by Douglas W. Hubbard and partially described in his book How to Measure Anything: Finding the Value of Intangibles in Business [D. Hubbard, How to Measure Anything: Finding the Value of Intangibles… …   Wikipedia