{ "modelVersion": "1.1.0", "illustrative": true, "actions": [ { "name": "Stage", "success": 30, "failure": -15, "expectedValue": 3 }, { "name": "Hold", "success": 0, "failure": 0, "expectedValue": 0 }, { "name": "Commit", "success": 100, "failure": -100, "expectedValue": -20 } ], "evWithout": 3, "evWithInformation": 25, "evPerfect": 40, "evpi": 37, "evsi": 22, "netInformationValue": 17, "branches": [ { "signal": "Positive test", "probability": 0.43, "posterior": 0.7906976744186046, "action": "Commit", "expectedValue": 58.13953488372093, "weightedValue": 25 }, { "signal": "Negative test", "probability": 0.57, "posterior": 0.10526315789473684, "action": "Hold", "expectedValue": 0, "weightedValue": 0 } ], "regret": [ { "name": "Commit", "success": 100, "failure": -100, "expectedValue": -20, "successRegret": 0, "failureRegret": 100, "expectedRegret": 60 }, { "name": "Stage", "success": 30, "failure": -15, "expectedValue": 3, "successRegret": 70, "failureRegret": 15, "expectedRegret": 37 }, { "name": "Hold", "success": 0, "failure": 0, "expectedValue": 0, "successRegret": 100, "failureRegret": 0, "expectedRegret": 40 } ], "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": "Hold", "expectedValue": 0 }, { "prior": 25, "bestAction": "Hold", "expectedValue": 0 }, { "prior": 30, "bestAction": "Hold", "expectedValue": 0 }, { "prior": 35, "bestAction": "Stage", "expectedValue": 0.75 }, { "prior": 40, "bestAction": "Stage", "expectedValue": 3 }, { "prior": 45, "bestAction": "Stage", "expectedValue": 5.25 }, { "prior": 50, "bestAction": "Stage", "expectedValue": 7.5 }, { "prior": 55, "bestAction": "Commit", "expectedValue": 10 }, { "prior": 60, "bestAction": "Commit", "expectedValue": 20 }, { "prior": 65, "bestAction": "Commit", "expectedValue": 30 }, { "prior": 70, "bestAction": "Commit", "expectedValue": 40 }, { "prior": 75, "bestAction": "Commit", "expectedValue": 50 }, { "prior": 80, "bestAction": "Commit", "expectedValue": 60 }, { "prior": 85, "bestAction": "Commit", "expectedValue": 70 }, { "prior": 90, "bestAction": "Commit", "expectedValue": 80 }, { "prior": 95, "bestAction": "Commit", "expectedValue": 90 }, { "prior": 100, "bestAction": "Commit", "expectedValue": 100 } ], "thresholds": [ { "actionA": "Commit", "actionB": "Stage", "prior": 54.83870967741935, "bestAction": "Commit" }, { "actionA": "Commit", "actionB": "Hold", "prior": 50, "bestAction": "Stage" }, { "actionA": "Stage", "actionB": "Hold", "prior": 33.333333333333336, "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": "3", "denominator": "1", "decimal": "3.000000000000000000000000000000000000000e0" }, "evWithInformation": { "numerator": "25", "denominator": "1", "decimal": "2.500000000000000000000000000000000000000e1" }, "evPerfect": { "numerator": "40", "denominator": "1", "decimal": "4.000000000000000000000000000000000000000e1" }, "evsi": { "numerator": "22", "denominator": "1", "decimal": "2.200000000000000000000000000000000000000e1" }, "evpi": { "numerator": "37", "denominator": "1", "decimal": "3.700000000000000000000000000000000000000e1" }, "netInformationValue": { "numerator": "17", "denominator": "1", "decimal": "1.700000000000000000000000000000000000000e1" }, "netSign": 1, "branches": [ { "signal": "Positive test", "mass": { "numerator": "43", "denominator": "100", "decimal": "4.300000000000000000000000000000000000000e-1" }, "posterior": { "numerator": "34", "denominator": "43", "decimal": "7.906976744186046511627906976744186046512e-1" }, "weightedValue": { "numerator": "25", "denominator": "1", "decimal": "2.500000000000000000000000000000000000000e1" }, "expectedValue": { "numerator": "2500", "denominator": "43", "decimal": "5.813953488372093023255813953488372093023e1" } }, { "signal": "Negative test", "mass": { "numerator": "57", "denominator": "100", "decimal": "5.700000000000000000000000000000000000000e-1" }, "posterior": { "numerator": "2", "denominator": "19", "decimal": "1.052631578947368421052631578947368421053e-1" }, "weightedValue": { "numerator": "0", "denominator": "1", "decimal": "0" }, "expectedValue": { "numerator": "0", "denominator": "1", "decimal": "0" } } ] }, "metrics": [ { "key": "without", "label": "Best value before information", "value": 3, "unit": "USDk", "detail": "" }, { "key": "evsi", "label": "Gross value of this test", "value": 22, "unit": "USDk", "detail": "Maximum justified test price under these payoffs." }, { "key": "net", "label": "Net information value", "value": 17, "unit": "USDk", "detail": "Gross information value less test cost." }, { "key": "evpi", "label": "Value of perfect information", "value": 37, "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": 100, "failure": -100, "expectedValue": -20, "successRegret": 0, "failureRegret": 100, "expectedRegret": 60 }, { "name": "Stage", "success": 30, "failure": -15, "expectedValue": 3, "successRegret": 70, "failureRegret": 15, "expectedRegret": 37 }, { "name": "Hold", "success": 0, "failure": 0, "expectedValue": 0, "successRegret": 100, "failureRegret": 0, "expectedRegret": 40 } ] }, { "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": 0.43, "posterior": 0.7906976744186046, "action": "Commit", "expectedValue": 58.13953488372093, "weightedValue": 25 }, { "signal": "Negative test", "probability": 0.57, "posterior": 0.10526315789473684, "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": "Hold", "expectedValue": 0 }, { "prior": 25, "bestAction": "Hold", "expectedValue": 0 }, { "prior": 30, "bestAction": "Hold", "expectedValue": 0 }, { "prior": 35, "bestAction": "Stage", "expectedValue": 0.75 }, { "prior": 40, "bestAction": "Stage", "expectedValue": 3 }, { "prior": 45, "bestAction": "Stage", "expectedValue": 5.25 }, { "prior": 50, "bestAction": "Stage", "expectedValue": 7.5 }, { "prior": 55, "bestAction": "Commit", "expectedValue": 10 }, { "prior": 60, "bestAction": "Commit", "expectedValue": 20 }, { "prior": 65, "bestAction": "Commit", "expectedValue": 30 }, { "prior": 70, "bestAction": "Commit", "expectedValue": 40 }, { "prior": 75, "bestAction": "Commit", "expectedValue": 50 }, { "prior": 80, "bestAction": "Commit", "expectedValue": 60 }, { "prior": 85, "bestAction": "Commit", "expectedValue": 70 }, { "prior": 90, "bestAction": "Commit", "expectedValue": 80 }, { "prior": 95, "bestAction": "Commit", "expectedValue": 90 }, { "prior": 100, "bestAction": "Commit", "expectedValue": 100 } ] }, { "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": 54.83870967741935, "bestAction": "Commit" }, { "actionA": "Commit", "actionB": "Hold", "prior": 50, "bestAction": "Stage" }, { "actionA": "Stage", "actionB": "Hold", "prior": 33.333333333333336, "bestAction": "Hold" } ] } ], "warnings": [], "summary": "Stage has the highest expected payoff before new evidence. The supplied test adds net expected value after its cost. The information-value ceiling is 37 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." ] }