Description
- Abstract:
- A number of problems of interest in applied mathematics and biology involve the quantification of uncertainty in computational and real-world models. A recent approach to Bayesian uncertainty quantification using transitional Markov chain Monte Carlo (TMCMC) is extremely parallelizable and has opened the door to a variety of applications which were previously too computationally intensive to be practical. In this dissertation, we first explore the machinery required to understand and implement Bayesian uncertainty quantification using TMCMC. We then describe four biological systems of interest and demonstrate that the methodology can be used to recover parameter values, discover relationships between the parameters, and select the model that best describes the observed data. To this end, we identify the locations of abnormalities in arterial blood flow networks, discover the origin of epidemics on a population network, determine which model best describes DNA methylation patterns, and recover values and correlations for parameters describing micro-swimmers in a viscous fluid.
- Notes:
- Thesis (Ph. D.)--Brown University, 2020
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Citation
Larson, Karen Ruth,
"Data-driven uncertainty quantification for problems in systems biology"
(2020).
Applied Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://repository.library.brown.edu/studio/item/bdr:1129395/
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Applied Mathematics Theses and Dissertations
Theses and Dissertations for the Applied Mathematics department....