Bayes' Theorem & Screening Lab
Probability & Decision
Base-Rate Fallacy
Understand why highly accurate predictive models and fraud detectors generate mostly false alarms when the underlying business event is rare.
⚡ Real-World Business Presets
Posterior Probability / Precision (PPV)
P(Genuine Event | Positive Alert)
P(Event | Alert) = TP / (TP + FP)
15.5%
Only 18 of 116 flagged cases are genuine
Natural Frequency Grid (Out of 1,000 Accounts / Events)
True Positive (18)
False Alarm (98)
Missed Event (2)
True Non-Event (882)
Contingency Matrix (Confusion Table)
| Model Decision | Actual Event Present (\(A\)) | Actual Non-Event (\(\neg A\)) | Marginal Total |
|---|---|---|---|
| Flagged Positive (\(B\)) |
True Positive (TP)
18
|
False Positive (FP)
98
|
116 |
| Flagged Negative (\(\neg B\)) |
False Negative (FN)
2
|
True Negative (TN)
882
|
884 |
| Marginal Total | 20 | 980 | 1,000 |
Positive Predictive Value (PPV)
15.5%
Reliability of a positive flag
False Discovery Rate (FDR)
84.5%
Share of alerts that are wasted false alarms
Negative Predictive Value (NPV)
99.8%
Reliability of an unflagged account
Model & Population Sliders
The natural prevalence of the event in the entire population (e.g. churners, fraud, rare diseases).
True Positive Rate: The probability that a true event triggers a positive alert.
True Negative Rate: The probability that a non-event is correctly left unflagged.