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Saturn: A Bayesian Example
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General Motors (GM) is launching a new car (Saturn) and is looking for a location and production site. After GM's location and real estate department has found its preferred site, it will assign a 'subjective' probability of .9 to this site suggesting that "we are 90% certain that Tennessee is superior to its closest competitors Michigan and New Jersey."
However, GM management is still sufficiently confident that this assessment is correct since it has relatively little prior knowledge of the state. It also does not want to give the impression of merely imitating Nissan's prior decision for Smyrna, relying too much on Nissan's experience or yielding to the Governor's persuasive abilities.
GM engages the FANTUS corporation, a large (formerly independent) location and corporate real estate consulting firm located in New Jersey (and acquired in 1996 by Deloitte & Touche), to carry out a quick survey and evaluation to confirm or reject its initial assessment. Fantus President Yaseen (of course a geographer by training) tells GM that the re-evaluation will be only 80% reliable because of time and measurement constraints and the limits GM has imposed on consulting fees. [In operational terms, if the evaluation comes out in favor of Tennessee, it will be with a probability of .8. If, on the other hand, Fantus favors either Michigan or N.J., Fantus will be 80% certain that Tennessee is an inferior location.
GM now wants to know what its own, revised pro-Tennessee probability will be after Fantus's collection of additional independent information and unbiased reevaluation:
In terms of Bayes' Theorem:
P(E1) = .9
F = "Location evaluation by Fantus inicates Tennessee is superior"; then the conditional probabilities ("likelihoods") are:
|P (F|E1) = .8|| ( = reliability of new information|
or the likelihood that new information supports the original hypothesis)
|P (F|E2) = .2|
|Posterior Probability = P (E1|F) =|| P(E1) P(F|E1)|
P(E1) P(F|E1) + P(E2) P(F|E2)
.9 x .8
.9 x .8 + .1 x .2
If the Fantus location survey indicates that Tennessee is superior, GM's new (posterior) probablity (confidence) should be .97
If, however, Fantus says: "Michigan or N.J. is a better location, what is GM's new probability (confidence) that Tennessee is still better?
|1 -||posterior probability that|
Michigan or N.J. is superior
|= 1 -|| .1 x .8
.1 x .8 + .9 x.2
|= .69 = posterior probability for Tennessee.|
Are you still surprised that GM did not come to Washington State?
Hayter, Roger. Dynamics of Industrial Location, 1997/98., p.299: "Creating core workforces in new locations: GM's Saturn plant"
Saturn Corporation: Our Story
http://www.microsoft.com/servers/evaluation/casestudies/SpringHill.asp (Spring Hill)
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