358. EVSI

Expected Value of Sample Information (EVSI) — value of imperfect information, like a market survey that updates (but doesn’t fully reveal) the state of nature.

The realistic counterpart of EVPI what most real-world decisions face.

358.1. Setup

You can run a test or survey before deciding. Each test outcome :

• Occurs with some probability

• Updates your beliefs about state via Bayes’ theorem:

After observing , you make the optimal decision given the updated beliefs:

358.2. EVSI formula

EVSI is always between and EVPI:

— at most EVPI (since no info beats perfect info), at least (you can always ignore the info).

358.3. Example

States (high demand), (low demand), with .

Test reliability:

• If , test says “high” with
• If , test says “high” with

Updates:

Given “test high” (probs ):

• :
• :
• Best: , value

Given “test low” (probs ):

• :
• :
• Best: , value

(vs EVPI )

So this test is worth at most \M. If it costs more, skip it.

358.4. Why EVSI < EVPI

The sample provides probabilistic updating, not certainty. Some test outcomes still leave significant ambiguity. EVPI assumes you’d be told exactly which state — much stronger.

358.5. Use cases

• Market research budgeting: should I commission a \K consumer survey? Compare EVSI to cost.
• Pilot programs: small-scale rollout to learn before full commitment
• Diagnostic tests: in healthcare, sequential decisions to test before treating
• A/B testing: when is the next experiment worth running?

358.6. Bayesian decision-making

EVSI is fundamentally Bayesian: it requires prior probabilities, likelihood functions, and updating. The Bayesian decision theory framework subsumes EVPI and EVSI as special cases of expected utility under updated beliefs.

358.7. See also

• EVPI — upper bound
• EMV
• Bayes’ Rule — the updating
• Decision Trees