Statistical Computing in Modern Scientific Analysis

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Modern-day scientific analyses employ ever more accurate instruments to record ever larger amounts of experimental data. While this has great promise for scientific discovery, extracting sound conclusions for complex and interacting instrumental errors poses a formidable challenge in statistical computing. The goal of this research program is to develop reliable measurement models for various dynamical processes in the natural sciences, and to develop the computational methods to use these models for scientific inquiry. A central focus of this research program is statistical inference for differential equations (DEs). DE models naturally and faithfully capture the underlying physics of countless dynamical processes. However, statistical inference for these models is extremely computationally intensive, and susceptible to large numerical round-off errors. This research program will address these issues by pursuing the following objectives: - Objective 1: To correctly account for round-off errors by incorporating them directly into the statistical model. - Objective 2: To effectively substitute DE models by surrogates for which inference is much more straightforward. - Objective 3: To develop approximate methods of inference for DEs using machine learning methods and toolkits. The path towards realizing these objectives will propose important methodological connections between a variety of DE models and otherwise isolated computational inference strategies. Addressing DE inference via machine learning methods will produce fast, flexible and reliable computational tools to promote widespread use of DEs for scientific inquiry -- in addition to providing excellent training for students to pursue impactful data science careers in the Canadian workforce.