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

Exchangeability means that the joint prior distribution is invariant under breed relabelling:for every permutation $\pi$. The labels carry no prior information about maximum size. This is reasonable for comparable breeds before observing their measurements when no covariates or biological knowledge distinguish them.

Exchangeability does not imply independence. In a hierarchical Bayesian model, the parameters can be independent conditional on a shared hyperparameter but dependent after it is integrated out. Known systematic biological differences would call for a model of those differences, with exchangeability only for the remaining unexplained variation.