IDEA FOUND // IDEA 08
Bayesian Updating
“Only 1% of transactions are fraudulent. A fairly accurate detector raises an alert. Is fraud almost certain?”
01 / PLAINLY
What it means, plainly
Bayesian updating starts with a prior probability and changes it according to how expected the new evidence would be under each hypothesis. The posterior result is still a probability, not certainty.
02 / CONTEXT
A little more
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.
03 / WHY IT MATTERS
Why it matters
It prevents test accuracy from being confused with the chance that a positive case is real, especially when the condition being detected is rare.
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.
04 / EXAMPLE
A familiar example
With 1% fraud, 90% sensitivity, and a 5% false-alarm rate, an alert means roughly a 15% chance of fraud—not 90%.
05 / LIMIT
What it does not mean
A prior need not be arbitrary, and the posterior still represents uncertainty.
06 / NOTICE
Notice it in your day
For the fraud example, make a table of true and false alerts using the stated prevalence, sensitivity, and false-alarm rate. Compare their counts before interpreting one alert.
FINAL NOTE
The idea worth keeping
Even an accurate test may create many false alarms when the condition it seeks is rare.
QUESTIONS / 02
Questions people still have
What is a prior probability?
It is the starting probability grounded in relevant information before the new evidence from the case is incorporated.
Does a sensitive test make a positive case almost certain?
Not necessarily. The posterior also depends on the prior prevalence and the test's false-alarm rate.
CHECK / 01