 Solution

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 ${\lambda }_i$ 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.