▶Forward probability
The likelihood asks how often warm sea-surface temperatures occur when a cyclone does or does not form.
Bayes' Theorem
From prior belief to posterior probability
Bayes' theorem combines what was plausible before an observation with how compatible that observation is under each possible explanation.
watchone idea
→manipulateone example
→leave withone intuition
The essential idea: evidence updates probability through likelihood, but the base rate still matters.
One Concept · One Example
What to notice
- The prior is belief before the new data.
- The likelihood scores compatibility with the data.
- The posterior is the normalized update.
Three probabilities that must not be confused
Reverse probability
The posterior asks how likely cyclone formation is after warm SST has been observed.
How much should warm water change the forecast?
Use the tropical-cyclone example from the video. Change the base rate and the two likelihoods, then watch the posterior update.
Prior cyclone probability5.0%
×Warm SST likelihood90.0%
÷Warm SST overall33.0%
=Posterior cyclone probability13.6%
| Cyclone | No cyclone | |
|---|---|---|
| Warm SST | 45 | 285 |
| Cooler SST | 5 | 665 |
A strong indicator can still imply a modest posterior probability when the event itself is rare or false positives are common.