EVPI, EVSI, and net learning value

Value of information asks a practical question: could learning before acting improve the decision enough to justify its money, time, delay, and other consequences? It values information only through decisions it may change—not through curiosity, confidence, or data volume.

Baseline and perfect information

First calculate the best expected value with current information, EV(current). Then imagine learning the relevant state perfectly before choosing and calculate EV(perfect information) by choosing the best included action separately in each state after human feasibility review.

EVPI = EV(perfect information) − EV(current) for a maximization problem.

Under one internally coherent model, EVPI cannot be negative. It is an upper bound on what perfect information about the modeled uncertainty could be worth—not a price recommendation and not the value of all possible research. If the result is materially negative, the state/action mapping, optimization direction, units, or calculation is inconsistent.

Imperfect or sample information

A real test, pilot, borehole program, market study, or inspection is imperfect. EVSI requires an observation model: for every true state, the conditional probability of every possible signal. Use Bayes’ rule to update state probabilities after each signal, select the best action for that signal, then average across signals.

EVSI = EV(with sample information) − EV(current)

Net learning value = EVSI − direct information cost

Under consistent assumptions before cost, 0 ≤ EVSI ≤ EVPI. Net learning value can be negative. Report schedule delay, option expiry, exposure during the study, participant burden, privacy, environmental impact, and implementation effort separately or incorporate them explicitly when the value model legitimately supports doing so.

Minimum valid inputs

• the decision that will occur after observing the signal;
• the uncertainty states and current prior probabilities;
• all possible test signals and P(signal | state), including false positives and false negatives;
• the feasible policy for each signal, with the same consequence model as the baseline;
• direct acquisition cost and decision-relevant non-monetary burdens;
• evidence and date for test performance, transferability, independence assumptions, and implementation timing.

Do not calculate EVSI by merely attaching a cost to an “information” branch. Without an observation model and posterior-dependent choices, the number is not EVSI. If the workbench represents learning as two complete strategies—act now versus acquire information—compare those strategies transparently and label the result according to what was actually modeled.

In the version 1 workbench, the stored noInformationBranchId is a structural act-now reference that confirms the learning record is anchored to a real non-information branch. It does not force that branch to be the numerical benchmark. The deterministic engine values the information strategy against the best modeled alternative at the same decision that is not declared as an information branch and reports the comparator actually used as baselineBranchId.

Decision rule and interpretation

A positive net learning value indicates that the modeled study improves expected value after direct cost. It does not mandate the study. Feasibility, deadlines, irreversibility, budget limits, safety, equity, legal duties, and model uncertainty may override the arithmetic. If information will not change any feasible action, its decision value is zero even if it is scientifically interesting.