Doctor of Philosophy
Statistics and Actuarial Sciences
Dean, Charmaine B.
University of Waterloo
Woolford, Douglas G.
Understanding the dynamics of wildfires contributes significantly to the development of fire science. Challenges in the analysis of historical fire data include defining fire dynamics within existing statistical frameworks, modeling the duration and size of fires as joint outcomes, identifying the how fires are grouped into clusters of subpopulations, and assessing the effect of environmental variables in different modeling frameworks. We develop novel statistical methods to consider outcomes related to fire science jointly. These methods address these challenges by linking univariate models for separate outcomes through shared random effects, an approach referred to as joint modeling. Comparisons with existing approaches demonstrate the flexibilities of the joint models developed and the advantages of their interpretations. Models used to quantify fire behaviour may also be useful in other applications, and here we consider modeling disease spread. The methodologies for wildfire modeling can be used, for example, for understanding the progression of Covid-19 in Ontario, Canada.
The key contributions presented in this thesis are the following: 1) Developing frameworks for modelling fire duration and fire size in British Columbia, Canada, jointly, both through modelling using shared random effects and also through copulas. 2) Illustrating the robustness of joint models when the true models are copulas. 3) Extending the framework into a finite joint mixture to classify fires into components and to identify the subpopulation to which the fires belong. 4) Incorporating the longitudinal environmental variables into the models. 5) Extending the method into the analysis of public health data by linking the daily number of Covid-19 hospitalizations and deaths as time series processes using a shared random effect. A key aspect of the research presented here is the focus on extensions of the joint modeling framework.
Summary for Lay Audience
This thesis develops novel statistical techniques for analyzing data associated with fire science and disease modeling. In general terms, a mathematical model can be used to describe relationships observed in the real world. We create modeling frameworks where different types of data (e.g. time to event occurrence and repeated environmental observations) can be incorporated into a single model.
Understanding how wildfires grow contributes to the development of fire science. Some research areas we study include analyzing historical fire data to learn how they behave, and studying predictive variables such as the time to supress the fire and the area burned. We also consider variables such as seasonality, location, and weather, and the impact of these variables on fire behaviour.
We use a technique called joint modeling that allows the incorporation of multiple types of data into one model simultaneously, and we build on this approach to describe fire behavior. Using this approach, we show the effect of predictive variables on two outcomes, duration and size of fires. Models used to quantify fire behaviour may also be useful in other applications, such as modeling disease spread. The methodologies for wildfire modeling can be used, for example, for understanding the progression of an infectious disease. We apply our techniques developed for studying fire science to the study of Covid-19 in Ontario, Canada.
Xi, Da Zhong, "Statistical Methods with a Focus on Joint Outcome Modeling and on Methods for Fire Science" (2020). Electronic Thesis and Dissertation Repository. 7536.