= Solution
Fit both hierarchies to the historical data and compare their <posterior predictive checks>. Use discrepancies sensitive to between-individual tails, such as the maximum standardized personal mean, tail counts and the spread of individual sample means. Simulate new individual means as well as repeated observations; conditioning only on fitted personal means would conceal a poor population model.
Leave whole individuals out for <cross-validation>, rather than just measurements, when the aim is prediction for a new individual. Compare held-out predictive log densities or interval calibration, with uncertainty in the comparison. Check both fits' <Markov chain Monte Carlo convergence diagnostics> and sensitivity to scale priors. Better tail prediction and adequate calibration would support the heavier-tailed model; the data are required to decide, so no empirical winner can be asserted here.
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