C6. Two kinds of interval
How do the probability statements for a 95% credible interval and a 95% confidence interval differ?
Worked answer (click to show)
Definitions/notation. A 95% credible interval C(x) satisfies \mathbb{P}(\theta\in C(x)\mid x)=0.95 under the specified model and prior. A 95% confidence procedure I(X) has 95% repeated-sampling coverage of a fixed \theta (exactly or approximately, as stated), rather than 95% posterior probability for its observed interval.