A credit desk can combine a prior default-rate estimate with new observed defaults. Bayes' rule turns that prior and the sample likelihood into a posterior distribution. This lesson works beta–binomial and normal–normal updates, then distinguishes posterior probability from frequentist confidence. Prior strength and likelihood assumptions determine how much the estimate changes.
Learning objectives. By the end of this note you should be able to:
- state posterior likelihood prior and identify prior, likelihood, evidence, and posterior;
- update a Beta prior through binomial data, and a normal prior through a normal mean;
- read prior parameters as pseudo-counts or pseudo-observations;
- compute a posterior mean default probability after observing a small sample.
In this lesson
- Bayes' theorem for a parameter
- Conjugate families
- Point summaries
- Credible intervals (brief)
- Prior as regulariser
Before you start
The full lesson, with worked examples and exercise solutions, is for members.
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