Statistical methods for dynamic systems

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Differential equation models are often built on scientific principles such as conservation of mass, energy and momentum, giving them easily interpretable parameters. Predator prey interactions, chemical reaction dynamics and epidemic outbreaks are typical examples of dynamics well described with differential equation models. Depending on the values of parameters and other inputs, a single differential equation model can describe a wide variety of behaviours such as oscillations, steady states and exponential growth and decay, giving them the flexibility to describe a system under a variety of conditions. However, the flexibility of this class of model comes at the price of difficult statistical challenges. This proposed statistical research is aimed at making differential equation models more accessible and informative by extending inference beyond parameter estimation. The proposed research develops the statistical technology to improve inference associated with differential equation models in areas of model selection, and inference about bifurcation points. Furthermore, this research proposes to extend lessons learned from analysis of differential equation models into spatio-temporal models and smoothing methods.