Time Series appear ubiquitous in sciences and society, including financial time series, time series of disease spreads or time series of key molecules regulating the life and death of cells, animals, and humans. A key challenge for data scientists and mathematicians is using the wealth of information in the time series to learn about the underlying system. However, a human-level understanding of the system requires mechanistic and causal information that can typically not be extracted from time series alone.
In this exciting project, we will advance the mathematical framework to use time series data to learn about causal and mechanistic relations of the underlying complex system. We will use the data for model selection and parameter inference of mechanistic mathematical models that describe the complex system and then use the models to make new predictions that can be validated with new data. This project will collaborate closely with experimental and industrial partners, depending on the candidates focusing more on biomedical, engineering or finance collaborators. For example, we will explore how signals in financial time series indicate the emergence of trends, how cell migration patterns indicate changes in cell behaviour, or how molecular patterns indicate responses to drugs. Mathematical techniques to be developed and/or applied will be from, e.g., causal inference, differential equation modelling, time series analysis, Bayesian methods.
Please contact [Email Address Removed] and [Email Address Removed] for further information, and submit your application at https://www.birmingham.ac.uk/postgraduate/courses/research/maths/applied-mathematics-phd.aspx .