Bayesian Value of Information Calculator

Measure perfect and sample information before expensive decisions. Review priors, test accuracy, utilities, and value. See outcomes instantly with graphs, tables, exports, and guidance.

Responsive calculator with EVPI, EVSI, posterior updates, CSV export, PDF export, and Plotly graph

Calculator Inputs

The page uses a stacked layout, while the calculator fields use 3 columns on large screens, 2 on medium, and 1 on mobile.

Enter payoffs in the same utility or monetary scale.

General Settings

State 1

State 2

State 3

State 4

Payoff Matrix by Action

Action 1

Action 2

Action 3

Action 4

Formula Used

Expected value of an action:
EV(a) = Σ [ P(state i) × Utility(a, state i) ]

Expected value without new information:
EVwoI = max EV(a)

Expected value with perfect information:
EVwPI = Σ [ P(state i) × max Utility(action, state i) ]

Expected value of perfect information:
EVPI = EVwPI - EVwoI

Posterior after a positive signal:
P(state i | +) = P(+ | state i) × P(state i) / P(+)

Expected value with sample information:
EVwSI = P(+) × max EV(a | +) + P(-) × max EV(a | -)

Expected value of sample information:
EVSI = EVwSI - EVwoI

Net sample information value:
Net EVSI = EVSI - information cost

How to Use This Calculator

  1. Choose how many uncertain states and decision actions you want to compare.
  2. Enter a name and prior probability for each state.
  3. Enter the probability that your study produces a positive signal in each state.
  4. Enter the payoff or utility for every action-state combination.
  5. Add the study cost to estimate net value after research expense.
  6. Press calculate to view EVPI, EVSI, posterior probabilities, best actions, tables, exports, and the Plotly graph.

Example Data Table

This example matches the default values loaded in the calculator.

State Prior P(Positive | State) Expand Capacity Maintain Current Plan Partner Externally
Strong Market 0.35 0.85 180000 125000 100000
Moderate Market 0.30 0.60 110000 95000 85000
Weak Market 0.20 0.35 30000 55000 70000

Add a fourth state or fourth action when you want a richer scenario analysis.

Frequently Asked Questions

1. What does EVPI tell me?

EVPI shows the maximum amount you should ever pay for perfect knowledge of the true state before choosing an action. It measures the cost of uncertainty in your current decision environment.

2. What does EVSI measure?

EVSI measures the expected benefit of imperfect information from a study, test, or signal. It compares your expected value after observing evidence against the best expected value without extra information.

3. Why do prior probabilities matter so much?

Priors control the baseline chance of each state before new evidence arrives. Different priors change action rankings, posterior probabilities, and the economic value of collecting more information.

4. Why is my net EVSI negative?

A negative net EVSI means your study cost is larger than the expected benefit of better decisions. In that case, the information may still be interesting, but it is not financially justified.

5. Can I use utilities instead of money?

Yes. The calculator works with any consistent payoff scale, including money, profit, utility points, or loss values. Just keep every payoff and cost in the same unit system.

6. What is expected opportunity loss?

Expected opportunity loss measures how much value you expect to give up by choosing an action instead of the best action for each state. The minimum EOL matches EVPI apart from rounding.

7. Why does the calculator normalize probabilities?

Users often enter priors that sum close to, but not exactly, one. The calculator rescales them to preserve relative beliefs and keep all Bayesian computations internally valid.

8. When should I collect more information?

Collect more information when the net EVSI is positive, the decision stakes are large, and the study meaningfully changes posterior beliefs. High noise and low decision sensitivity usually reduce value.

Related Calculators

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.