3 ms·
Ah, yes. It's the Dempster-Shafer theory example in the case of high conflict. The complete/original example goes as follows: "Suppose that one has two equi-
by espeed 10y ago
Ah, yes. It's the Dempster-Shafer theory example in the case of high conflict.
The complete/original example goes as follows:
"Suppose that one has two equi-reliable doctors and one doctor believes a patient has either a brain tumor, with a probability (i.e. a basic belief assignment—bba's, or mass of belief) of 0.99; or meningitis, with a probability of only 0.01. A second doctor believes the patient has a concussion, with a probability of 0.99, and believes the patient suffers from meningitis, with a probability of only 0.01. Applying Dempster’s rule to combine these two sets of masses of belief, one gets finally m(meningitis)=1 (the meningitis is diagnosed with 100 percent of confidence)."
https://en.wikipedia.org/wiki/Dempster–Shafer_theory#Example_producing_counter-intuitive_results_in_case_of_high_conflict https://en.wikipedia.org/wiki/Dempster–Shafer_theory#Example...
- defen 10y agoI understand the math that is going on there, but I think in the real world I would question the reliability of both of the doctors and begin to wonder if I didn't actually have Lupus. In other words, what mechanism is there for questioning the underlying sample space?
- gizmo686 10y agoThat is certainly a possibility. But the situation is much more reasonable if you imagine that the doctors ran different tests. For example, suppose we have a prior probability of: Tumor - .49, Concussion - .49, meningitis - .02. The first doctor performs an MRI that conclusively proves that there is no Tumor. He now conludes that there is a 96% chance of concussion, and 4% chance of meningitis. The second doctor performs a cognitive test that conclusively proves there is no concussion, but a 96% chance of tumor, and 4% chance of menigitis. If we combine these two tests, we have disproven the two post likely causes, so the less likely cause becomes reasonable. This doesn't work out quite so nicely in reality because of false negatives and (as you point out) the non 0% chance of an unspecified disease. Also, ideally you would tell the second doctor about the first test.