Bayesian analysis for some hierarchical linear models

The importance of hierarchical modelling and Markov chain Monte Carlo algorithms has grown enormously over the last several years. We discuss using such algorithms to simulate from the posterior distribution of the parameters in hierarchical linear models with respect to specific examples. The basic computational paradigm is developed in detail and then (with some novel departures) is applied in two different settings: heteroscedasticity in forecasting U.S. Presidential elections and spatial random effects models for home radon levels. Posterior simulations can be extremely sensitive to the choice of model so we take care to check model fit and investigate the effects of departures from the model in each case.