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Title of the thesis: Bayesian ordinary differential equation and Gaussian process modeling of biomedical data

Thesis defender: Juho Timonen
Opponent: Professor Magnus Rattray, University of Manchester, UK
Custos: Professor Harri Lähdesmäki, Aalto University School of Science

Mathematical modeling of biomedical data helps us understand complex biological processes and disease development. This doctoral thesis explores different ways of modeling biomedical data collected over time while accounting for measurement uncertainty and patient-specific variability.

The aim of the research is to develop flexible probabilistic models that, once fitted to data, are more informative than the raw measurements alone. Such models make it possible to understand the phenomenon under study, decompose it into interpretable components, and predict the behavior of the system being analyzed. Because fitting these models to data is often computationally demanding, the development of reliable yet efficient computational methods is also a central theme of the thesis.

The thesis analyzes, for example, proteins measured from patients’ blood during disease progression using models that include separate components for measurement noise, explanatory variables such as age and sex, and the stage of disease development. These components are constructed to be flexible yet easily interpretable, enabling assessment of the effects of different factors. The research also develops and compares methods for model reduction, allowing the number of model components to be decreased while retaining predictive accuracy, thereby improving interpretability and usability.

In addition, the thesis highlights limitations of commonly used numerical solvers in probabilistic models and develops a reliable and efficient workflow for fitting models that rely on such solvers. The approach is shown to be useful for fitting differential equation models, facilitating the analysis of for example gene regulatory networks, drug distribution in the body, and the spread of infectious diseases.

Overall, the research combines statistical modeling, computational efficiency, and biological interpretability in a way that complements and extends existing methods. The developed methods and software packages can be applied broadly to the analysis of disease progression as well as to data modeling in many other fields.

Keywords: Bayesian inference, differential equation, Gaussian process, longitudinal data

Contact information: +358443200039 and juho.timonen@iki.fi 

Thesis available for public display 7 days prior to the defence at .