You’ll see two kinds of “95% interval” in the wild, and they’re built completely differently:
- A Bayesian credible interval: a range that contains 95% of the posterior’s probability mass. It’s read directly off the posterior distribution you actually computed — no repeated-sampling story required.
- A frequentist confidence interval: a range built from a procedure that, if you re-ran the whole data-collection-and-interval-construction process many times, would contain the true parameter 95% of the time. Crucially, this is a claim about the procedure, averaged over hypothetical repetitions — not a claim about the one interval you actually got.
They can even come out numerically identical for simple problems with uninformative priors. But what they’re entitled to claim is different, and this is one of the most commonly botched interpretations in applied statistics — people say the confidence-interval sentence (“95% probability the true value is in here”) when what they built was a confidence interval, which technically doesn’t support that sentence at all (the true parameter either is or isn’t in any specific realized interval — there’s no probability left once the data is in hand; the 95% describes the long-run procedure, not this one outcome).
Your posterior credible interval is [0.61, 0.74]. Because you built it as a Bayesian credible interval — literally the range covering 95% of your posterior’s probability mass — which interpretation below is actually correct for it?