= Credible set
{title2=$\mathbb P(\theta\in C\mid x)=1-\alpha$}
A <credible set> is a measurable set of parameter values containing specified <posterior probability>. At credibility level $1-\alpha$, it satisfies $\int_C\pi(\theta\mid x)d\theta=1-\alpha$ for a continuous posterior. A <credible interval> is a credible set that is an interval. Equal-tailed and highest-density choices add selection rules; the posterior-mass requirement alone does not make the set unique. Its probability statement is conditional on the observed data and prior model, whereas a frequentist <confidence interval> is interpreted through repeated-sample coverage.
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