As has been well-discussed, the explosion of interest in Bayesian methods over the last ten to twenty years has been the result of the convergence of modern computing power and efficient Markov chainMonte Carlo (MCMC) algorithms for sampling from posterior distributions. Practitioners trained in traditional, frequentist statistical methods appear to have been drawn to Bayesian approaches for two reasons. One is that Bayesian approaches implemented with the majority of their informative content coming from the current data, and not any external prior information, typically have good frequentist properties (e.g., low mean squared error in repeated use). But perhaps more importantly, these methods as now readily implemented in WinBUGS and other MCMC-driven packages now offer the simplest approach to hierarchical (random effects) modeling, as routinely needed in longitudinal, frailty, spatial, time series, and a wide variety of other settings featuring interdependent data.