One-sided credible interval ($(-\infty ,F^{-1}(1-\alpha )]$)

A one-sided credible interval puts all excluded posterior probability in one tail. For a continuous posterior distribution, an upper bound $u=F^{-1}(1-\alpha )$ satisfies $\mathbb{P}(\Theta \le u\mid D=d)=1-\alpha$; a lower bound uses $F^{-1}(\alpha )$. Intersecting with the parameter's allowed range removes points of zero posterior probability. For the beta distribution $\mathrm{Beta}(10,4)$, the upper 95% bound is $u\approx 0.887334219$, so $[0,u]$ is the alternative credible interval shown above.