Uncertainty in Cost Estimates. Joseph B. Kadane Carnegie Mellon University email@example.com. “Prediction is difficult, especially about the future” Niels Bohr Robert Storm Peterson Yogi Berra Samuel Goldwyn Mark Twain Outline: Uncertainty in general An example in another field
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Joseph B. Kadane
Carnegie Mellon University
Robert Storm Peterson
Suppose you are uncertain about the weather in Pittsburgh tomorrow and in particular about whether it will rain, and whether the high temperature will exceed 80° F. Then there are 4 uncertain events:
One and only one of the will occur, i.e. they are mutually exclusive and disjoint.
Imagine that you can buy or sell tickets that pay $1 if occurs, and $0 if does not occur. At what price would you be willing to buy or sell such a ticket?
Hence you avoid being a sure loser if and only if your prices obey the laws of probability.
Suppose there are tickets that pay $1 if A and B both occur, $0 if A occurs but B does not, and the price is returned if A does not occur. Suppose you would pay for such a ticket.
Physics is touted as the most exact of sciences, one in which uncertainty is best controlled. However, as we’ll see, experimental physicists routinely assume that the measurements they make have no systematic errors, and are routinely wrong, by hindsight, in that assessment.
None of these are apparent to the experimenter at the time.
Repeating an experiment many times can reduce the “random error” associated with an average, but does nothing for systematic error. The culture of physics has not traditionally encouraged a discussion of the likely magnitude of systematic error.
“A reported value whose accuracy is entirely unknown is worthless”
Why is it that cost estimates of almost anything are so rarely too high, and very often too low? One simple correction is to multiply the cost estimate by .
If an interval is required, multiply by where
Perhaps it is possible to do better than this with a more thoughtful approach.
What are some of the sources of uncertainly in estimating the cost of large, long-term projects?
Technology risk: the technology to do the project may not currently exist. How much may it cost to produce the technology? What happens if the technological issues cannot be resolved?
Economic and political changes: If cost estimates are in current dollars, what effect may future inflation have? What may be the effects of legislative or regulatory changes? What assumptions underlie the project? What are the consequences if those assumptions are wrong?
D.V. Lindley, Understanding Uncertainty, J. Wiley & Sons.
Principles of Uncertainty, Chapman and Hall, 2011, also free on the web at my website http://www.uncertainty.com.
M. Henrion and B. Fischoff, “Assessing uncertainty in physical constants,” American Journal of Physics, 54(9), September, 1986.