All numeric cases below are synthetic teaching examples, not empirical research findings.
Example: informative milestone
| P(C)=0.4, P(U | C)=0.6, P(U | not C)=0.1 imply P(U)=0.3. IG=h(0.3)-0.4h(0.6)-0.6h(0.1), about 0.1466098512 nats, or 24.0004% of maximum information. |
Example: dramatic but rare
A spectacular indicator with a large conditional effect may have low expected value when it almost never occurs. Include the negative branch and indicator probability before ranking.
Example: incoherent elicitation
A prior of 0.7 with c=0.5,a=0.8,b=0.2 contradicts total probability, which gives 0.5. Stop and reconcile; the helper must not return a fabricated validated VOI.
Counterexample
“Indicator A has 10% information and B has 10%, therefore together they provide 20%” ignores redundancy.