Visualization and Joint Analysis of Monitored Multivariate Spatio-Temporal Data with Applications to Forest Fire Modelling and Sports Analytics

This thesis develops and applies novel techniques for the study of complex data structures with applications to wildland fire analytics and sports analytics. We consider situations where different models share information, including many different variables recorded simultaneously in aerial wildland fire fighting, how the frequency and severity of wildland fires are related, and how the shot locations of hockey players can be decomposed into spatial components that are shared across different players. The first study analyzes flight patterns while fighting a wildland fire using several outlier detection techniques. These techniques applied several definitions of ``outlier\u27\u27 to determine whether or not the pilot did something different while dropping water on a fire. To aid in fire management, we developed a tool to display the outliers in a way that is meaningful to the managers. Our second set of studies analyzes the association between ignitions of wildland fires (temporally and spatially, respectively) and the total area burned by those fires. We used a modelling approach that allows two models to share information in order to get a better estimate of the underlying process and elucidate underlying relationships. The first version of this analysis models the number of fires per day, and the second version models the number of fires in any arbitrary region. The association between ignition probability and size is not always positive; in some time periods or regions there is a negative association indicating that high ignition probability is associated with small fires. Furthermore, our techniques may suggest a change in our ability to detect and measure fires. Our final study moves away from wildland fire and into sports analytics. We employ the spatial techniques used in the previous analysis to characterize shot locations in the National Hockey League (NHL). These techniques were augmented with image recognition algorithms to summarize the spatial distribution of shots as a collection of coefficients for a collection of estimated basis functions. A definition of shot quality was created based on the coefficients for the spatial distribution of goals. Each of the papers contained in this thesis are applications of spatial, temporal, or spatio-temporal techniques to multivariate data with a new methodological extension. The aerial fire fighting paper provides visualizations to summarize a variety of statistical process control techniques; the wildland fire ignition papers provide joint modelling approaches for temporal and spatial point processes, respectively; and the hockey paper summarizes the similarities between a large number of spatial point processes