Evaluation of diagnostics for hierarchical spatial statistical models
In the twenty-first century, we are able to build large, complex statistical models that are very much like the scientific processes they represent. We use diagnostics to highlight inadequacies in the statistical model, and because of the complexity many different diagnostics are needed. This is analogous to the process of diagnosis in the medical field, where a suite of diagnostics is used to assess the health of a patient. This chapter is focused on evaluating model diagnostics. In the medical literature, a structured approach to diagnostic evaluation is used based on measurable outcomes such as sensitivity, specificity, ROC curves, and false discovery rate. We suggest using the same framework to evaluate model diagnostics for hierarchical spatial statistical models; and we make the observation that a different curve, which we have called the Discovery (DSC) curve, gives another way to evaluate a diagnostic. For a spatial model, the True negatives and False positives are defined in our proposed evaluation procedure through cross-validation.