MGMT20005 Chap.3 Information Value and Bayesian Updating
Information Value and Bayesian Updating
Week 3 asks whether uncertainty is worth reducing. Expected value with perfect information allows a different best action in each state and creates an upper bound on what state-revealing information can be worth. Sample information is imperfect: a report has different conditional probabilities under different states, so Bayes' theorem converts priors into posteriors.
The calculation flows from prior and conditional probabilities to joint probabilities, from joints to the marginal probability of the report, and from joint over marginal to posterior. Those posteriors feed a contingent strategy, with one best action after each report. EVSI compares the gross expected value of that strategy with the best action without information.
The acquisition fee is then compared with the benefit or deducted once, never twice.
What this chapter covers
- 01
Expected value without information as the baseline
- 02
Expected value with perfect information and EVPI
- 03
Prior, conditional, joint, marginal and posterior probabilities
- 04
Bayes tables for favourable and unfavourable reports
- 05
Contingent strategies after sample information
- 06
EVSI, information cost and the perfect-information ceiling
Worked example · free
Update demand after a warning report
- 2Volatile-and-Warning joint probability = 0.30 times 0.80 = 0.24.
- 2Stable-and-Warning joint probability = 0.70 times 0.20 = 0.14.
- 2P(Warning) = 0.24 plus 0.14 = 0.38. This is the marginal denominator shared by both posterior calculations.
- 2P(Volatile | Warning) = 0.24/0.38 = 0.6316 and P(Stable | Warning) = 0.14/0.38 = 0.3684. The posteriors sum to one.
Key terms
- Perfect information
- Information that reveals the true state before the decision is made.
- EVPI
- The expected-value gain from perfect information over the best fixed action without it.
- Sample information
- An imperfect report that changes probabilities without identifying the state with certainty.
- Prior probability
- A state probability assessed before the new report or evidence is observed.
- Joint probability
- The probability that a state and a report occur together, found by multiplying prior and conditional probability.
- Posterior probability
- An updated state probability conditional on the report that was observed.
- EVSI
- The gross expected-value gain from an optimised strategy using sample information.
Information Value and Bayesian Updating FAQ
What does the expected value of perfect information limit?
It limits the rational price of information that perfectly reveals the uncertain state represented in the model. EVPI is the expected value with state-contingent best actions minus the best expected value without information. An imperfect survey or pilot should not be assigned greater decision value than that perfect-information ceiling.
Why are conditional and posterior probabilities different?
They condition in opposite directions. P(report | state) describes report accuracy when the state is assumed known. P(state | report) describes belief about the state after a report is observed. Bayes' theorem connects them through the prior state probability and the marginal probability of the report.
How is the probability of a report calculated?
Multiply each state prior by the conditional probability of that report under the state, producing mutually exclusive joint probabilities. Add those joints across all states. The sum is the marginal report probability and becomes the denominator for every posterior under that same report.
Can information have zero value even when probabilities change?
Yes. If the same action remains optimal after every possible report, the report does not improve the decision even though posterior probabilities may move substantially. Information value comes from the flexibility to choose a better action, not merely from producing a different probability estimate.
Exam move
Use one Bayes table for every report outcome. Put states in rows and the columns in a fixed order: prior, conditional report probability, joint, report marginal and posterior. Check that priors sum to one, that the report marginal lies between zero and one, and that posteriors under one report sum to one. Then build the information decision tree from the inside out.
Choose the best action separately within each report branch using the relevant posterior probabilities, weight those retained branch values by the probabilities of the reports, and compare the total with the no-information baseline. Keep EVSI gross until the end, then compare it with the fee or subtract the fee once. State what EVPI or EVSI implies for the maximum price or acquisition decision.
Rehearse the same signal twice, once favourable and once unfavourable, so you experience the changing denominator. Before calculating EVSI, write the policy in conditional language: which action follows each report. Then calculate the report probabilities and verify they sum to one. This makes the outer expectation auditable and stops the report from being treated as if it revealed the state.
Working through Information Value and Bayesian Updating in MGMT20005? Sia is AskSia’s AI Management tutor — ask any MGMT20005 Information Value and Bayesian Updating question and get a clear, step-by-step explanation grounded in how MGMT20005 is taught and assessed. Read this chapter free, then take your hardest questions to Sia.
