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Bayesian Updating
“Only 1% of transactions are fraudulent. A fairly accurate detector raises an alert. Is fraud almost certain?”
01 / SUMMARY
In short
Bayesian reasoning combines a prior probability with how much more likely the evidence is under one hypothesis than its alternatives. Evidence updates what we knew; it does not erase the base rate or turn uncertainty into certainty.
02 / SEQUENCE
What happens
- 01
Begin with a prior rate grounded in relevant information.
- 02
Compare how expected the evidence is if each hypothesis were true.
- 03
Update the probability and keep it open to new evidence.
03 / SCENE
In the wild
With 1% fraud, 90% sensitivity, and a 5% false-alarm rate, an alert means roughly a 15% chance of fraud—not 90%.
04 / LIMIT
The limit
A prior need not be arbitrary, and the posterior still represents uncertainty.
FINAL NOTE
What remains
Even an accurate test may create many false alarms when the condition it seeks is rare.
CHECK / 01
Put it to work
How firm is your read?