= Poisson-uniform posterior mean
{c}
{title2=$\mathbb E[\Lambda\mid x_1,\ldots,x_n]=\frac{\int_l^u t^{s+1}e^{-nt}\,dt}{\int_l^u t^se^{-nt}\,dt}$}
For a uniform <prior distribution> on $(l,u)$ with $0<l<u$, conditionally independent <Poisson distribution> observations have sufficient count $s=\sum_i x_i$. Their <Bayesian posterior> density is proportional to $t^s e^{-nt}$ on that bounded interval. The displayed <posterior mean> is the <Bayes estimator under squared error loss>, and is generally not the affine <Bühlmann credibility estimate>.
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