= Bounded uniform-location posterior
{title2=$\theta\mid\mathbf x\sim\operatorname{Unif}(\max(A,x_{\max}-d),\min(B,x_{\min}+d))$}
For independent observations uniform on $(\theta-d,\theta+d)$ and a uniform prior on $(A,B)$, the <likelihood> is constant wherever all data-compatible intervals overlap. The posterior is therefore uniform on the displayed intersection, provided it has positive length. Both squared-error and absolute-error Bayes estimates are its midpoint. An empty or zero-length interval has zero marginal <likelihood> and cannot be normalized into this ordinary posterior density.
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