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Title: Bayesian inference for stable differential equation models with applications in computational neuroscience
Author: Maybank, Philip
ISNI:       0000 0004 7966 7608
Awarding Body: University of Reading
Current Institution: University of Reading
Date of Award: 2019
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Inference for mechanistic models is challenging because of nonlinear interactions between model parameters and a lack of identifiability. Here we focus on a specific class of mechanistic models, which we term stable differential equations. The dynamics in these models are approximately linear around a stable fixed point of the system. We exploit this property to develop fast approximate methods for posterior inference. We first illustrate our approach using simulated EEG data on the Liley et al model, a mechanistic neural population model. Then we apply our methods to experimental EEG data from rats to estimate how parameters in the Liley et al model vary with level of isoflurane anaesthesia. More generally, stable differential equation models and the corresponding inference methods are useful for analysis of stationary time-series data. Compared to the existing state-of-the art, our methods are several orders of magnitude faster, and are particularly suited to analysis of long time-series (>10,000 time-points) and models of moderate dimension (10-50 state variables and 10-50 parameters).
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral