Incorporating Scientific Priors in Hierarchical Spatio-Temporal Models: An Invasive Species Case Study

There is increasing interest in predicting ecological processes. Methods to accomplish such predictions must account for uncertainties in observation, sampling, models, and parameters. Statistical methods for spatio-temporal processes are powerful, yet difficult to implement in complicated, high-dimensional settings. However, recent advances in hierarchical Bayesian formulations for such processes can be utilized for ecological prediction. These formulations are able to account for the various sources of uncertainty, and can incorporate scientific judgment in a probabilistically consistent manner. For example, analytical diffusion models can serve as motivation for the hierarchical model for invasive species. We demonstrate by example that such a framework can be utilized to predict spatially and temporally, population characteristics of birds from the Breeding Bird Survey. Time permitting, alternative specifications of underlying process will be considered.