Computationally efficient hierarchical spatial models for large datasets: A case study for the assessment of forest characteristics across the Lake States

The scientific community is moving into an era where data rich environments provide extraordinary opportunities to understand the spatial complexity of ecological processes. Across scientific fields, researchers face the challenge of coupling these data with imperfect models to better understand variability in their system of interest. In the environmental sciences there is recognized urgent need to develop and disseminate methodology capable of accurately accounting for multiple sources of uncertainty. Accordingly, the goal of this thesis was to explore and illustrate the properties of promising new modeling tools that will enable researchers to extract more information from large spatial datasets. In particular, this thesis was motivated by a larger project's need to analyze a large forest inventory dataset with the intent to better understand the potential of managing forests for increased complexity as a climate change mitigation and adaptation strategy. The thesis yields results from the analysis of synthetic and forestry datasets that clearly demonstrate how model misspecification, specifically ignoring spatial dependence among model residuals, can result in incorrect inference about regression parameters of interest. These results have important implications for hypothesis testing and ultimately forest management and policy decisions. The thesis details some modeling tools and useful guidelines that allow practitioners to more fully accommodate model assumptions and draw correct inference for large spatial datasets.