Value of Distribution-Family Information

This experimental workflow asks whether a decision would improve if the correct member of a declared set of distribution families were learned perfectly. It first integrates parameter and outcome uncertainty inside every family. It then optimizes once under the current probability mixture and once inside each family after the family index is revealed.

For family probabilities p_m and comparable conditional expected values Q[m,a], the maximizing form is:

current  = max_a sum_m p_m Q[m,a]
resolved = sum_m p_m max_a Q[m,a]
gross VDI = resolved - current
net VDI = gross VDI - information cost

This is discrete-index EVPPI presented under issue #557’s VDI name. It is not distributional-equity VOI, full structural EVPI (which would also resolve within-family uncertainty), goodness-of-fit/model selection, or imperfect model-discrimination EVSI.

Run the exact fixture

The repository-relative fixture path below is available from a source checkout. Installed-wheel users should supply the same JSON request from their own path; the installed Python schema and CLI perform the same strict validation.

voiage --format json calculate-value-of-distributional-information \
  specs/frontier/value-of-distributional-information/v1/fixtures/normative/input.json \
  --output vdi-result.json

The synthetic fixture has two equally probable families and two alternatives. The current decision is B with value 9, the family-resolved expected value is 11, gross VDI is 2, and the declared information cost of 0.5 gives signed net VDI 1.5, all in net-benefit-point units.

The request must give each candidate family a structured definition, parameterization, within-family integration method, sources, data reference and value transformation. It must also name probabilities and their source, the common alternatives, value unit and direction. The five comparability IDs (population, horizon, discounting, value semantics and cost location) must be affirmatively verified with an evidence reference.

Version 1 accepts only exact enumerated conditional expectations, recorded in conditional_value_assurance; a simulation or uncertain estimate cannot be relabelled as exact. Probabilities are never inferred or silently renormalized. The result preserves the assurance and comparability records, returns complete numerical tie sets, and labels exact enumeration as exact rather than reporting a fabricated standard error. The checked-in result schema is available from a source distribution or repository checkout; the wheel installs the input schema and evaluator but does not separately advertise a result-schema resource.

Python is the only executable surface. Rust, R and Julia remain unsupported, Mojo is external, and scientific review of the terminology, partition and probability provenance is required before stable promotion.