Solution
= Solution
A $100(1-\alpha)\%$ <credible set> is a measurable subset $C(x)\subseteq(0,1)$ with posterior <probability> $1-\alpha$:
$$
\boxed{\int_{C(x)}\pi(\theta\mid x)\,d\theta=1-\alpha.}
$$
In ordinary language, \b[given the observed data and the chosen prior model, the <probability> that the parameter lies in this set is $1-\alpha$]. Such a set need not be an interval or be unique; its defining requirement is posterior mass.