Information Pricing

What is it worth to know before you decide? Build a model, simulate it and price the uncertainty. Everything runs in your browser.

Run

Downloads every simulated scenario: inputs, intermediates, each decision's reward and opportunity loss, and the optimal reward.

Run first.

Inputs

The things you're unsure about, each with a distribution. Pick Fixed for a number you already know.
Lognormal
Exponential
Uniform
Fixed

Decisions

The options you choose between, how each one is labelled, and the reward to maximise.
Values
  • 30
  • 40
  • 50
  • 60
  • 70

Intermediates

Named formulas that reuse inputs, other intermediates or the decision. Use them to break up a long reward.

None yet. Add one to name a step of the reward.

Dataflow

How the numbers feed each other, from inputs down to the reward. Click a box to find its row and light up what it uses and what uses it.

6 nodes and 5 arrows. Reward uses N, t, T, P, C.

Dataflow

How it works

List what you don't know as inputs, then your options and a reward formula. Press Run to score every option over many scenarios. The best option's average regret is what perfect information is worth. The value chart and the policy tree show which input is worth resolving.

The definitions are in the docs, and the background in Pricing Information.

References

  1. Raiffa, H. & Schlaifer, R. (1961). Applied statistical decision theory. Division of Research, Harvard Business School. Where opportunity loss and the expected value of perfect information first got their names and their maths.
  2. Howard, R. A. (1966). Information value theory. IEEE Transactions on Systems Science and Cybernetics 2(1). Information is worth what it saves you on the decision, and never more than knowing everything.
  3. Hubbard, D. W. (2010). How to measure anything: Finding the value of "intangibles" in business (2nd ed.). Wiley. The pitch for this tool: price a measurement by the expected opportunity loss it removes before you pay for it.
  4. Brennan, A., Kharroubi, S., O'Hagan, A. & Chilcott, J. (2007). Calculating partial expected value of perfect information via Monte Carlo sampling algorithms. Medical Decision Making 27(4). The value of learning one input, done the slow way with simulations inside simulations.
  5. Strong, M. & Oakley, J. E. (2013). An efficient method for computing single-parameter partial expected value of perfect information. Medical Decision Making 33(6). Sort the scenarios by one input, cut them into groups and pick the best decision per group: one simulation is enough.
  6. Sadatsafavi, M., Bansback, N., Zafari, Z., Najafzadeh, M. & Marra, C. (2013). Need for speed: An efficient algorithm for calculation of single-parameter expected value of partial perfect information. Value in Health 16(2). Another take on the same shortcut, confirming that grouping the samples you already have gives good answers fast.
  7. Breiman, L., Friedman, J. H., Olshen, R. A. & Stone, C. J. (1984). Classification and regression trees. Wadsworth (reissued by Chapman & Hall/CRC). The policy tree grows the classic way: try every cut on every input and keep the best one.
  8. Athey, S. & Wager, S. (2021). Policy learning with observational data. Econometrica 89(1). Why a simple rule that picks a decision per situation, judged by its average regret, is the right thing to learn.
  9. Zhou, Z., Athey, S. & Wager, S. (2023). Offline multi-action policy learning: Generalization and optimization. Operations Research 71(1). Shallow trees that choose among many decisions, checked on scenarios they never saw.
  10. Felli, J. C. & Hazen, G. B. (1998). Sensitivity analysis and the expected value of perfect information. Medical Decision Making 18(1). An input can swing the outcome a lot and still not change the decision; the scatter shows both sides.
  11. Oakley, J. E. (2009). Decision-theoretic sensitivity analysis for complex computer models. Technometrics 51(2). Ask which inputs matter for the decision, not just for the output: the right-hand axis of the scatter.
  12. Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M. & Tarantola, S. (2008). Global sensitivity analysis: The primer. Wiley. How much an input moves the output is the spread of the output's average given that input.
  13. Plischke, E., Borgonovo, E. & Smith, C. L. (2013). Global sensitivity measures from given data. European Journal of Operational Research 226(3). That spread can be read straight off the simulated scenarios by grouping them, with no extra runs.
  14. Kelley, T. L. (1935). An unbiased correlation ratio measure. Proceedings of the National Academy of Sciences 21(9). A correction so an input that doesn't matter scores about zero instead of picking up noise.
  15. Hörmann, W. (1993). The generation of binomial random variates. Journal of Statistical Computation and Simulation 46(1–2). Counts are drawn exactly and quickly, even for large numbers of trials.