The reported 95% <credible interval> for $\beta_1$ is
$$
[-0.33,\,2.37].
$$
Conditional on the model, prior, and observed data, its posterior probability is 0.95. A frequentist 95% <confidence interval> instead has 95% coverage under repeated sampling before the data are observed; it does not assign a sampling probability to the fixed parameter after observing this dataset.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 218 / 6 / e / Solution

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A credible interval is an interval whose <posterior probability> equals a prescribed level. Conditional on the observed data and the Bayesian model, the unknown parameter lies in the interval with that probability.

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