ABSTRACT
This chapter presents a quintessential hierarchical model to set the stage for specific forms of ecological data. Bayesian methods are incredibly powerful for building and fitting hierarchical models that can accommodate mechanisms in the underlying process, the parameters, and the measurement instrumentation used to observe the process. The design of hierarchical models accounts for these so-called repeated measures on each individual in a way that explicitly addresses measurement uncertainty, pseudo-replication, and different amounts of individual-level uncertainty due to varying sample sizes. Hierarchical models provide a formal mechanism to incorporate random effects because; they treat the individual-level parameters as the random effect. The David Lunn Method involves fitting hierarchical models with many data-level models in two stages. The first stage involves fitting the set of nonhierarchical data-level models independently using placeholder priors for model parameters. The second stage involves a substantially simplified Markov chain Monte Carlo algorithm to fit the full hierarchical model using the output from the first stage.
