UFO Occurrence Base-Rate Simulator 3D

Base-Rate Fallacy — 3D

True anomaly base rate 1 in 10,000

Report reliability P(report|anomaly) 95%

False-positive rate P(report|mundane) 3%

Naive intuited P(anomaly)

–

Bayesian posterior P(anomaly)

–

Reports observed

— from genuine cluster

— from mundane cluster (false positives)

How it works

The gold cluster is the tiny population of genuinely anomalous events; the gray cloud is the vastly larger population of mundane look-alikes (aircraft, drones, satellites, balloons). Both populations flash "reports" — the gold cluster at its report-reliability rate, the gray cloud at its false-positive rate. Drag to orbit and watch which color the report flashes actually come from most often.

P(anomaly|report) =
   P(report|anomaly)·P(anomaly)
 ───────────────────────────────────────────
   P(report|anomaly)·P(anomaly) + P(report|mundane)·P(mundane)

True anomaly base rate — how many points are in the gold cluster relative to the gray cloud.
Report reliability — how often each gold point flashes as a report.
False-positive rate — how often each gray point flashes as a report. Even a small rate applied to a huge cloud produces more total flashes than a high rate applied to a tiny cluster.

This is the same arithmetic behind the medical-testing base-rate fallacy: a "99%-accurate" test still returns mostly false positives when the condition being tested for is rare enough. The scene doesn't lie about individual reports — each flash genuinely came from a real or a mundane point — but the count of flashes, not their individual reliability, is what determines the true probability.

Genuine anomaly point Mundane point True-positive flash False-positive flash

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UFO Occurrence Base-Rate Simulator (3D)