Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 34 / 1 / e / Solution

Use the intended hierarchical Bayesian model: the breed parameters are conditionally independent given $\alpha ,\beta$, and observations are independent given their breed parameters. Put $m_i=\max (\beta ,M_i)$. The uniform-Pareto model evidence factorizes over breeds:Identical marginal prior distributions alone would not determine this product; conditional independence is the additional assumption.