Functions & Formulae

Each applied formula has its own function page, with a signature, implementations, and tests.

Value of information function

v(NB_d(theta)) = EVPI

Maps the joint distribution of net benefit across the options in a decision to the expected gain from resolving some or all of the uncertainty before choosing, compared with choosing the option with the highest expected net benefit on current information.

  • Per-person EVPI from probabilistic draws

    EVPI = sum_(s=1)^S [NBmax_s] / S - ENB_cur

    Averages, over S equally weighted draws, the highest net benefit available in each draw, the value of choosing with perfect information, and subtracts the highest expected net benefit among the options, the value of the decision made on current information. The result is the expected opportunity loss of the current decision per person and an upper bound on the value of research for that person.

  • Population EVPI over the decision's lifetime

    EVPI_pop = EVPI * sum_(t=0)^T [N_t / (1+r)^t]

    Multiplies per-person EVPI by the discounted number of people expected to face the decision in each period while it remains relevant. The result is compared with the cost of research: when it is below the cost of any feasible study, further research is not worthwhile on these grounds.

  • EVPPI for a subset of parameters

    EVPPI_phi = E_phi[max_d E_(psi|phi)[NB_d(phi,psi)]] - max_d E_(phi,psi)[NB_d(phi,psi)]

    Values perfect information about a subset phi of the parameters, with the remaining parameters psi still uncertain. The inner expectation averages net benefit over psi given phi, the maximum picks the best option for that value of phi, the outer expectation averages over phi, and the value of the current decision is subtracted. The expected value of sample information replaces knowledge of phi with the data from a proposed study.