Ewch i’r prif gynnwys

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

This research project is in competition for funding with one or more projects available across the EPSRC Doctoral Training Partnership (DTP). Usually the projects which receive the best applicants will be awarded the funding. Find out more information about the DTP and how to apply.

Application deadline: 15 March 2019

Start date: 1 October 2019

The goal of this project is to build new stochastic models for the EEG data using stochastic processes, namely heavy-tailed diffusion and fractional diffusion.

Electroencephalogram (EEG) is a record of electrical activity generated by a large number of cortical neurons in the brain. The supervisors have real-world EEG data from African children affected by cerebral malaria, as well as data on subsequent neurodevelopmental and cognitive outcomes of these children. The over-arching goal of the project is to build new stochastic models for the EEG data using stochastic processes, namely heavy-tailed diffusion and fractional diffusion. The proposed new mathematical methods will result in estimation of the EEG parameters, which could predict which children would have neurocognitive deficits after surviving cerebral malaria.

Background

The heavy-tailed and diffusion and fractional diffusion models are novel and powerful models of stochastic processes incorporating properties of classical and anomalous diffusions. These  models can be supported by Electroencephalogram (EEG) data described above. The identification problem can be solved by using generalised method of moments, martingale estimation function method and quasi-likelihood method will be used and the results will be compared.

Preliminary analyses of the available EEG data indicate that the increments of EEG recordings for some channels have a normal distribution or  Student distribution. Student distribution is a heavy-tailed distribution, so it is preferred for modelling the distribution of recordings in which extreme jumps in brain activity are much more common. Much more interesting histograms are symmetric with two or even three peaks, indicating that the distribution of increments of EEG recordings should be modelled with a new symmetric multi-modal distribution.

Within this research problem, based on analysis of EEG recordings and the suitable distribution of their increments, two types of stochastic models will be studied:

  1. Stationary mean-reverting diffusions with the prescribed marginal distribution suggested by the shape of the histogram of increments of the EEG signal, satisfying the specific stochastic differential equations.
  2. Fractional diffusion models characterised by the fractional Fokker-Planck equations.

For parameter estimation of these processes, generalised method of moments, martingale estimation method, and quasi-likelihood method will be used. The performance of these methods will be compared, and parameters estimated using the best method will be related to other medical and developmental data available to the supervisors.

Project aims and methods

The heavy-tailed and diffusion and fractional diffusion models are novel and powerful models of stochastic processes incorporating properties of classical and anomalous diffusions. These  models can be supported by Electroencephalogram (EEG) data described above. The identification problem can be solved by using generalised method of moments, martingale estimation function method and quasi-likelihood method will be used and the results will be compared.

The main objective of the project is to develop stochastic models for the EEG data while advancing the theory of heavy-tailed and anomalous diffusion. Specifically, new limit theorems and statistical procedures  will be developed and applied to real-life problems.

Prof. N.Leonenko, Prof. A.Sikorskii and Dr. B. Gauthier are well-known experts in the theory of fractional diffusion and statistical inference for stochastic processes.

Goruchwylwyr

Photograph of Professor Nikolai Leonenko

Yr Athro Nikolai Leonenko

Professor

Email:
leonenkon@caerdydd.ac.uk
Telephone:
+44 (0)29 2087 5521
Dr Bertrand Gauthier photograph

Dr Bertrand Gauthier

Lecturer

Email:
gauthierb@caerdydd.ac.uk
Telephone:
+44(0)29 2087 5544

Co-supervisors

Professor A Sikorskii, Michigan State University.

Gwybodaeth am y Rhaglen

I gael gwybodaeth am strwythur y rhaglen, gofynion mynediad a sut i wneud cais ewch i’r rhaglen Mathemateg.

Gweld y Rhaglen
Mae'r Academi Ddoethurol yn falch i'ch gwahodd chi i'w Gŵyl Ymchwil Ôl-raddedig cyntaf.

Rhaglenni cysylltiedig

Dolenni perthnasol