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Summary: Extending Bayesian Theory to Cooperative Groups University of California Irvine (April 2, 2010) 1
Extending Bayesian Theory to Cooperative Groups:
an introduction to Indeterminate/Imprecise Probability Theories [IP]
also see www.sipta.org
Teddy Seidenfeld Carnegie Mellon University
based on joint work with Jay Kadane and
Mark Schervish
Extending Bayesian Theory to Cooperative Groups University of California Irvine (April 2, 2010) 2
Review from the earlier presentation.
In our examination of the Linear Pool combining probabilistic opinions into a
convex combination of those distributions we illustrated its failure to be
"Externally Bayesian." There two experts judged events A and S independent,
Pi(AS) = Pi(A)Pi(S) for i = 1, 2. But the Linear Pool created a group opinion
P3 with positive dependence. P3(A|S) > P3(A).
· Pooling and conditioning do not commute!
Extending Bayesian Theory to Cooperative Groups University of California Irvine (April 2, 2010) 3
We used this fact to give a simple decision problem with these features.
Choose among three treatment plans, {T1, T2, T3}, for a patient whose
allergic state {A, Ac
} has different probabilities for the two experts. The
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