= Uniform-Pareto model evidence
{title2=$p(y\mid\alpha,\beta)=\alpha\beta^\alpha/[(\alpha+n)m^{\alpha+n}]$}
For positive observations and $m=\max(\beta,\max_jy_j)$, the <Bayesian model evidence> follows by integrating the <uniform distribution> likelihood against a <Pareto distribution> prior. For independent groups with shared fixed <hyperparameters>, these evidences multiply. The resulting <hyperparameter> log likelihood is $I\log\alpha-\sum_i\log(\alpha+n_i)-\alpha\sum_i\log(m_i/\beta)$ up to a constant.
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