ABSTRACT
Hierarchical smoothing methods result in shrinkage of estimates for each unit towards the average outcome rate in the population within which exchangeability is assumed; shrinkage will be greater for units with observations based on small samples. Borrowing strength may need to be modified to account for, or accommodate, unusual observations. This chapter focuses on discrete mixture modelling, where the Bayesian approach has been coupled with many advances. A widely applied conjugate hierarchical scheme assumes normal sampling of observations and normally distributed latent effects. Hierarchical models for pooled inferences or density estimation based on a single underlying population with a specific parametric form are often a simplification. The normal-normal model may be robustified against skewness, heavy tails, and outlier studies in either the sampling density or the latent effects density. Parameter sampling via Markov chain Monte Carlo is facilitated by conjugate prior choices for the mixing density.
