Stochastic models for increments of EEG recordings using heavy-tailed and multimodal diffusions

Salinger, Zeljka 2023. Stochastic models for increments of EEG recordings using heavy-tailed and multimodal diffusions. PhD Thesis, Cardiff University. Item availability restricted.

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Abstract

Electroencephalography (EEG) is a useful diagnostic tool for many brain disorders, including coma. EEG signals are non-stationary, but it is possible to model EEG signal increments using stationary processes. In this thesis, EEG increments are viewed as discrete time observations from a diffusion process with marginal distributions which is independent of time. First, the basic theory needed for modelling of the diffusion processes is presented. Then, based on the histograms of EEG increments, the choice of a marginal distribution is the generalized Gaussian distribution (GGD) with a parametrization that comprises both light-tailed and heavy-tailed distributions. Some properties of the GGD are presented, along with the method of estimation of the tail index using the socalled empirical scaling function. The estimated parameters from models across EEG channels obtained from both subfamilies are explored as potential predictors of neurocognitive outcomes in children 6 months after recovering from cerebral malaria. To include a wider range of marginal distributions observed in histograms, a new strictly stationary strong mixing diffusion model with marginal multimodal (three-peak) distribution and exponentially decaying autocorrelation function is used for modelling of EEG increments. The marginal distribution is viewed as a mixture of three non-central generalized Gaussian distributions. Distribution parameters are estimated using the expectation-maximization (EM) algorithm, where the added shape parameter is estimated using the higher order statistics approach based on an analytical relationship between the shape parameter and the kurtosis. Similarly to the unimodal case, obtained estimates are then used for prediction of subsequent neurodevelopment and cognition of cerebral malaria survivors using the elastic net regression. All predictive models are compared to determine whether additional information obtained from multimodality of the marginal distributions can be used to improve the prediction. The results of analysis in this thesis show that stochastic modelling of EEG features can improve the explanation of variation in neurodevelopmental outcomes of children who were in coma due to cerebral malaria.

Item Type:	Thesis (PhD)
Date Type:	Completion
Status:	Unpublished
Schools:	Mathematics
Funders:	EPSRC
Date of First Compliant Deposit:	8 February 2024
Last Modified:	08 Feb 2024 10:24
URI:	https://orca.cardiff.ac.uk/id/eprint/166187

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