This is the final exam for The Value of Information. It pulls the whole course together: the change-my-action test that prices any piece of information, EVPI as the ceiling a perfect answer would buy you, EVSI as the honest price of a noisy test after Bayes deflates it, the three conditions that decide when a test is worth gathering, and the pitfalls that trick people into paying for information that changes nothing. Several questions look easy until you notice the test can’t move your decision, or the base rate is quietly diluting your survey. Reason each one through — and where there are numbers, actually compute.
How this exam works
Read carefully — this exam is final. Each question appears one at a time. Once you submit an answer it is locked for good: there is no going back, no retry, and no restart. Your score is hidden until the end, where you will see a pass/fail verdict. The pass mark is 70%. A few questions ask you to select all correct answers.
What is the value of a piece of information, in one line?
Select an answer to continue.
Course Recap
Big picture
The Value of Information — the whole model
- Value of Information
- The core test
- Value = best decision WITH minus best decision WITHOUT
- Always >= 0, capped by the stakes
- Cannot change your action -> worth 0
- Accurate is not the same as valuable
- EVPI (the ceiling)
- Value of a perfect, certain answer
- No real test can beat it
- Equals expected cost of the mistake you would make
- Shrinks toward 0 as the prior gets lopsided
- EVSI (pricing a noisy test)
- Test = sensitivity + specificity
- Bayes flips P(signal | state) into P(state | signal)
- Base-rate dilution: 80% accurate -> 73% sure
- Pre-posterior: weight each signal by how often it fires
- EVSI <= EVPI; net = EVSI minus price
- When it is worth it
- Genuine uncertainty
- A close decision
- High stakes
- Zero out any one -> value collapses
- Information as a real option: buy before you commit
- Pitfalls
- The cost of delay
- Analysis paralysis
- Accurate test of the wrong question
- Base-rate neglect overvalues noisy tests
- Rationalised-away or too-late info is worth 0
- The core test
Key takeaways
Information is worth exactly what it lets you do differently: the best decision with it minus the best decision without it. That value is never negative, always capped by the stakes, and drops to zero the moment a test cannot change your action — however accurate or cheap it is. EVPI prices a perfect answer and sets the ceiling no real test can beat; it equals the expected cost of the mistake your prior would otherwise commit you to, and it fades as you grow more certain. EVSI prices a noisy test after Bayes deflates its accuracy through the base rate, and you only buy when EVSI clears the price. Gathering information pays off only when genuine uncertainty, a close decision, and high stakes all hold at once — so treat a test as a real option, and watch for the traps: delay, paralysis, accurate answers to the wrong question, base-rate neglect, and information that arrives too late to matter.