Bayes' theorem: posterior probability from a prior, sensitivity and false-positi...

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{ "example": { "asOf": "2026-10-11T14:44:16.580Z", "degraded": false, "disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.", "falseAlarmShareOfPositives": 0.922360248447205, "falsePositiveRate": 0.096, "likelihoodRatioPositive": 8.333333333333334, "naturalFrequencies": { "falseNegatives": 20, "falsePositives": 950, "haveHypothesis": 100, "population": 10000, "trueNegatives": 8950, "truePositives": 80 }, "notChecked": [ "whether the rates apply to the person or case in question (they are population averages)", "repeated or dependent tests (the formula assumes one independent piece of evidence)", "…1 more" ], "posteriorGivenNegative": 0.002229753835176596, "posteriorGivenPositive": 0.07763975155279504, "posteriorOdds": 0.08417508417508418, "prior": 0.01, "priorOdds": 0.010101010101010102, "probabilityOfPositive": 0.10303999999999999, "reasons": [ "P(H | positive) = P(+|H) P(H) / [P(+|H) P(H) + P(+|not H) P(not H)].", "A low base rate means most positives are false positives, even with a good test (base-rate fallacy).", "…1 more" ], "sensitivity": 0.8, "source": "computed locally (Bayes' theorem)", "specificity": 0.904, "summary": "Prior 1.000%, sensitivity 80.0%, false-positive rate 9.60%: a positive result means a 7.76% chance the hypothesis is true.", "verdict": "STRONG_UPDATE" }, "type": "json" }