Hierarchical Bayesian Models for Predicting the Spread of Ecological Processes

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 spatiotemporal processes are powerful, yet difficult to implement in complicated high-dimensional settings. However, recent advances in hierarchical 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. In particular, 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, the relative population abundance of House Finches over the eastern United States.