Track 16 · Advanced Foundations · Lesson 3 of 8
Credible intervals
Compute equal-tailed and highest-posterior-density credible intervals and posterior tail probabilities, and interpret them correctly — including how they differ from confidence intervals.
A pricing team wants to tell a director “the conversion rate at 49 SAR is between 5.4% and 7.4%”, and the director asks: “How sure are you?” A credible interval answers that question directly — as a probability about the rate, given the data and the stated prior.
A posterior distribution is the complete answer of a Bayesian analysis, but reports need a summary. A credible interval is an interval that contains the parameter with a stated posterior probability, such as 95%. There are many intervals with 95% posterior probability; two choices are standard.
Included with a Formula Quest membership
It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Compute equal-tailed and HPD credible intervals from a Beta posterior
- Explain when the HPD interval differs from the equal-tailed one
- Calculate and use posterior probabilities such as P(θ > target)
- Interpret a credible interval correctly and contrast it with a confidence interval
- Treat Bayes factors with caution because of their prior sensitivity