Past exam of the mathematics course of the University of Cambridge 2008 iii Paper 44 3 j Solution 2026-10-14
The Student t-distribution has heavier tails than the normal distribution, so unusual personal means need not force the entire population's spread upward or be shrunk as strongly toward its center. The latent allows a large local prior variance for an outlying individual. This normal scale mixture representation of Student t is a useful robust version of the hierarchical Bayesian model. It still assumes a symmetric, unimodal population; a genuinely multimodal population may need a different model.