Mathematical models are used to describe and explore complex processes in many fields, including the study of disease dynamics in a population and the study of the wind-born spread of pollutants from power plants. Continuing advances in remote sensing and data collection have made it possible to collect data on similar processes at resolutions that were impossible a generation ago. Statistics and Data Science are fields focused on the analysis of data to inform decision making and scientific inquiry, but the most common methods used, such as linear regression or machine learning methods, cannot easily use mathematical models in their analysis approach. In this work, the PI will develop methods that make it easier to analyze data from systems where mathematical models are useful to describe the process in question. The methods developed include statistical approaches for modeling data in common forms, such as yearly averaged pollution concentrations over space, or the current number of individuals hospitalized with a disease. These methods will improve our ability to understand and predict complex behavior in spatial epidemiology, disease modeling, and ecology. Potential results include better estimates of epidemiological parameters such as the rate at which individuals contract a disease but do not show symptoms, which is critical for predicting the future of an epidemic. The project will provide research training opportunities for graduate students.
The use of mechanistic process models, like ODEs, SDEs, and PDEs, is central to the mathematical analysis of ecological and epidemiological processes. However, their use in statistical inference is relatively limited. In this work, the PI will develop statistical methods useful for analyzing data when the governing process is scientifically known to follow a mechanistic process model. As part of this work, the PI will develop methods for joint inference of individual-level data (like individual animal movement data) with population-level data (like population-level counts of animal abundance) with formal links between these two data streams and a single process model. In addition, the PI will develop methods for modeling data that come from an assumed stochastic process, like a diffusion model or a spatial disease spread model, but are collected as either a snapshot in time or an average over time (i.e., yearly average pollutant concentration). Together these projects will provide increased ability to specify and fit mechanistic statistical models to data common in a wide variety of scientific disciplines. This work will advance the ability of scientists to model data obtained in a variety of common formats using mechanistic models with interpretable parameters.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
|Effective start/end date||8/1/20 → 7/31/23|
- National Science Foundation: $210,000.00