= Binomial likelihood-power annealing
{title2=$p\sim\operatorname{Beta}(s/T+1,mn/T-s/T+1)$}
For $m$ independent <binomial distribution> observations with fixed trial count $n$ and total successes $s$, the likelihood-power <probability density function> relative to $dp$ is $p^{s/T}(1-p)^{(mn-s)/T}$. Its normalized law is the displayed <beta distribution>. Its mean tends to $s/(mn)$ and its variance tends to zero as $T\downarrow0$, including endpoint maxima. Energy for maximizing a <log-likelihood> is its negative; the opposite sign reverses the optimization.
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