{ "modelVersion": "1.1.0", "illustrative": true, "actions": [ { "name": "Hold", "success": 0, "failure": 0, "expectedValue": 0 }, { "name": "Stage", "success": 70, "failure": -15, "expectedValue": -8.2 }, { "name": "Commit", "success": 180, "failure": -100, "expectedValue": -77.6 } ], "evWithout": 0, "evWithInformation": 0, "evPerfect": 14.4, "evpi": 14.4, "evsi": 0, "netInformationValue": -4, "branches": [ { "signal": "Positive test", "probability": 0.532, "posterior": 0.13533834586466165, "action": "Hold", "expectedValue": 0, "weightedValue": 0 }, { "signal": "Negative test", "probability": 0.468, "posterior": 0.017094017094017096, "action": "Hold", "expectedValue": 0, "weightedValue": 0 } ], "regret": [ { "name": "Commit", "success": 180, "failure": -100, "expectedValue": -77.6, "successRegret": 0, "failureRegret": 100, "expectedRegret": 92 }, { "name": "Stage", "success": 70, "failure": -15, "expectedValue": -8.2, "successRegret": 110, "failureRegret": 15, "expectedRegret": 22.6 }, { "name": "Hold", "success": 0, "failure": 0, "expectedValue": 0, "successRegret": 180, "failureRegret": 0, "expectedRegret": 14.4 } ], "priorSweep": [ { "prior": 0, "bestAction": "Hold", "expectedValue": 0 }, { "prior": 5, "bestAction": "Hold", "expectedValue": 0 }, { "prior": 10, "bestAction": "Hold", "expectedValue": 0 }, { "prior": 15, "bestAction": "Hold", "expectedValue": 0 }, { "prior": 20, "bestAction": "Stage", "expectedValue": 2 }, { "prior": 25, "bestAction": "Stage", "expectedValue": 6.25 }, { "prior": 30, "bestAction": "Stage", "expectedValue": 10.5 }, { "prior": 35, "bestAction": "Stage", "expectedValue": 14.75 }, { "prior": 40, "bestAction": "Stage", "expectedValue": 19 }, { "prior": 45, "bestAction": "Commit", "expectedValue": 26 }, { "prior": 50, "bestAction": "Commit", "expectedValue": 40 }, { "prior": 55, "bestAction": "Commit", "expectedValue": 54 }, { "prior": 60, "bestAction": "Commit", "expectedValue": 68 }, { "prior": 65, "bestAction": "Commit", "expectedValue": 82 }, { "prior": 70, "bestAction": "Commit", "expectedValue": 96 }, { "prior": 75, "bestAction": "Commit", "expectedValue": 110 }, { "prior": 80, "bestAction": "Commit", "expectedValue": 124 }, { "prior": 85, "bestAction": "Commit", "expectedValue": 138 }, { "prior": 90, "bestAction": "Commit", "expectedValue": 152 }, { "prior": 95, "bestAction": "Commit", "expectedValue": 166 }, { "prior": 100, "bestAction": "Commit", "expectedValue": 180 } ], "thresholds": [ { "actionA": "Commit", "actionB": "Stage", "prior": 43.58974358974359, "bestAction": "Commit" }, { "actionA": "Commit", "actionB": "Hold", "prior": 35.714285714285715, "bestAction": "Stage" }, { "actionA": "Stage", "actionB": "Hold", "prior": 17.647058823529413, "bestAction": "Hold" } ], "informationEvaluation": { "policy": "Exact rational action rankings, signal masses, information values and net-value sign from canonical JSON-number decimals. Values displayed in charts and metrics are Number approximations. Probability and payoff uncertainty remains outside this arithmetic guarantee.", "evWithout": { "numerator": "0", "denominator": "1", "decimal": "0" }, "evWithInformation": { "numerator": "0", "denominator": "1", "decimal": "0" }, "evPerfect": { "numerator": "72", "denominator": "5", "decimal": "1.440000000000000000000000000000000000000e1" }, "evsi": { "numerator": "0", "denominator": "1", "decimal": "0" }, "evpi": { "numerator": "72", "denominator": "5", "decimal": "1.440000000000000000000000000000000000000e1" }, "netInformationValue": { "numerator": "-4", "denominator": "1", "decimal": "-4.000000000000000000000000000000000000000e0" }, "netSign": -1, "branches": [ { "signal": "Positive test", "mass": { "numerator": "133", "denominator": "250", "decimal": "5.320000000000000000000000000000000000000e-1" }, "posterior": { "numerator": "18", "denominator": "133", "decimal": "1.353383458646616541353383458646616541353e-1" }, "weightedValue": { "numerator": "0", "denominator": "1", "decimal": "0" }, "expectedValue": { "numerator": "0", "denominator": "1", "decimal": "0" } }, { "signal": "Negative test", "mass": { "numerator": "117", "denominator": "250", "decimal": "4.680000000000000000000000000000000000000e-1" }, "posterior": { "numerator": "2", "denominator": "117", "decimal": "1.709401709401709401709401709401709401709e-2" }, "weightedValue": { "numerator": "0", "denominator": "1", "decimal": "0" }, "expectedValue": { "numerator": "0", "denominator": "1", "decimal": "0" } } ] }, "metrics": [ { "key": "without", "label": "Best value before information", "value": 0, "unit": "USDk", "detail": "" }, { "key": "evsi", "label": "Gross value of this test", "value": 0, "unit": "USDk", "detail": "Maximum justified test price under these payoffs." }, { "key": "net", "label": "Net information value", "value": -4, "unit": "USDk", "detail": "Gross information value less test cost." }, { "key": "evpi", "label": "Value of perfect information", "value": 14.4, "unit": "USDk", "detail": "Upper bound for any information about these two states." } ], "tables": [ { "title": "Action payoffs, value and regret", "columns": [ { "key": "name", "label": "Action", "unit": "" }, { "key": "success", "label": "Success payoff", "unit": "USDk" }, { "key": "failure", "label": "Failure payoff", "unit": "USDk" }, { "key": "expectedValue", "label": "Expected payoff", "unit": "USDk" }, { "key": "successRegret", "label": "Success regret", "unit": "USDk" }, { "key": "failureRegret", "label": "Failure regret", "unit": "USDk" }, { "key": "expectedRegret", "label": "Expected regret", "unit": "USDk" } ], "rows": [ { "name": "Commit", "success": 180, "failure": -100, "expectedValue": -77.6, "successRegret": 0, "failureRegret": 100, "expectedRegret": 92 }, { "name": "Stage", "success": 70, "failure": -15, "expectedValue": -8.2, "successRegret": 110, "failureRegret": 15, "expectedRegret": 22.6 }, { "name": "Hold", "success": 0, "failure": 0, "expectedValue": 0, "successRegret": 180, "failureRegret": 0, "expectedRegret": 14.4 } ] }, { "title": "Bayes test branches", "columns": [ { "key": "signal", "label": "Signal", "unit": "" }, { "key": "probability", "label": "Branch probability", "unit": "" }, { "key": "posterior", "label": "Posterior success probability", "unit": "" }, { "key": "action", "label": "Preferred action", "unit": "" }, { "key": "expectedValue", "label": "Conditional expected payoff", "unit": "USDk" }, { "key": "weightedValue", "label": "Weighted contribution", "unit": "USDk" } ], "rows": [ { "signal": "Positive test", "probability": 0.532, "posterior": 0.13533834586466165, "action": "Hold", "expectedValue": 0, "weightedValue": 0 }, { "signal": "Negative test", "probability": 0.468, "posterior": 0.017094017094017096, "action": "Hold", "expectedValue": 0, "weightedValue": 0 } ] }, { "title": "Prior probability policy sweep", "columns": [ { "key": "prior", "label": "Prior success", "unit": "%" }, { "key": "bestAction", "label": "Preferred action", "unit": "" }, { "key": "expectedValue", "label": "Best expected payoff", "unit": "USDk" } ], "rows": [ { "prior": 0, "bestAction": "Hold", "expectedValue": 0 }, { "prior": 5, "bestAction": "Hold", "expectedValue": 0 }, { "prior": 10, "bestAction": "Hold", "expectedValue": 0 }, { "prior": 15, "bestAction": "Hold", "expectedValue": 0 }, { "prior": 20, "bestAction": "Stage", "expectedValue": 2 }, { "prior": 25, "bestAction": "Stage", "expectedValue": 6.25 }, { "prior": 30, "bestAction": "Stage", "expectedValue": 10.5 }, { "prior": 35, "bestAction": "Stage", "expectedValue": 14.75 }, { "prior": 40, "bestAction": "Stage", "expectedValue": 19 }, { "prior": 45, "bestAction": "Commit", "expectedValue": 26 }, { "prior": 50, "bestAction": "Commit", "expectedValue": 40 }, { "prior": 55, "bestAction": "Commit", "expectedValue": 54 }, { "prior": 60, "bestAction": "Commit", "expectedValue": 68 }, { "prior": 65, "bestAction": "Commit", "expectedValue": 82 }, { "prior": 70, "bestAction": "Commit", "expectedValue": 96 }, { "prior": 75, "bestAction": "Commit", "expectedValue": 110 }, { "prior": 80, "bestAction": "Commit", "expectedValue": 124 }, { "prior": 85, "bestAction": "Commit", "expectedValue": 138 }, { "prior": 90, "bestAction": "Commit", "expectedValue": 152 }, { "prior": 95, "bestAction": "Commit", "expectedValue": 166 }, { "prior": 100, "bestAction": "Commit", "expectedValue": 180 } ] }, { "title": "Pairwise policy intersections", "columns": [ { "key": "actionA", "label": "Action A", "unit": "" }, { "key": "actionB", "label": "Action B", "unit": "" }, { "key": "prior", "label": "Prior at equal value", "unit": "%" }, { "key": "bestAction", "label": "Best of all actions at intersection", "unit": "" } ], "rows": [ { "actionA": "Commit", "actionB": "Stage", "prior": 43.58974358974359, "bestAction": "Commit" }, { "actionA": "Commit", "actionB": "Hold", "prior": 35.714285714285715, "bestAction": "Stage" }, { "actionA": "Stage", "actionB": "Hold", "prior": 17.647058823529413, "bestAction": "Hold" } ] } ], "warnings": [ "This test has no decision value under the supplied actions and prior. Evidence can be informative without changing the preferred action." ], "summary": "Hold has the highest expected payoff before new evidence. The supplied test costs more than the decision value it creates. The information-value ceiling is 14.4 USDk for perfect state knowledge.", "methods": [ "Expected value = prior × success payoff + (1 − prior) × failure payoff.", "Bayes updates the prior separately after a positive and negative test. Branches of probability zero have no posterior.", "EVSI = expected best payoff after the imperfect test − best payoff before it. EVPI is the analogous value of perfect state knowledge.", "Net information value = EVSI − test cost. Payoffs are assumed to exclude this test cost.", "Joint signal-state masses, action rankings, EVSI, EVPI and the net-value sign use exact rational arithmetic for canonical decimal inputs. Only an exact zero is labelled break-even.", "Tied action values use literal name order independent of browser language for consistent display; this ordering does not establish a strict payoff advantage." ], "limitations": [ "Binary states, a single test, user-calibrated probabilities and risk-neutral expected monetary value.", "No repeated sampling, behavioural utility, ambiguity aversion or causal proof.", "Charts and headline values are numeric displays of exact rational results. Decimal input values are assumptions; risk-neutral economic comparison does not establish acceptable action or calibrated probability.", "Numerical input precision: use zero or absolute values of at least 0.000000001. Smaller nonzero inputs are rejected explicitly." ] }