http://theses.ncl.ac.uk/jspui/handle/10443/5374 2026-04-23T19:02:57Z 2026-04-23T19:02:57Z Binks, Rachel Louise http://theses.ncl.ac.uk/jspui/handle/10443/6744 2026-04-23T10:39:05Z 2025-01-01T00:00:00Z

Title: Bayesian inference on the order of stationary vector autoregressions with application to multivariate modelling of electroencephalography data Authors: Binks, Rachel Louise Abstract: Vector autoregressions (VARs) are widely used for modelling multivariate time series. VARs have an associated order p; given observations at the preceding p time points, the variable at time t is conditionally independent of all earlier history. The model order is therefore intrinsic to the characterisation of the process. It is common to assume a VAR is stationary, which requires the means, variances and covariances of the process to be constant over time. This can be enforced by imposing the stationarity condition which restricts the parameter space of the autoregressive coefficients to the stationary region. However, implementing this constraint is difficult as the stationary region has a complex geometry. Fortunately, pioneering recent work has provided a solution for enforcing stationarity in autoregressions of fixed order p based on a reparameterisation in terms of a set of interpretable and unconstrained transformed partial autocorrelation matrices. In this research, focus is placed on the difficult problem of allowing p to be unknown, developing priors and computational inference that take full account of order uncertainty. To this end, a comparison of existing approaches for determining the order of station ary univariate autoregressions is provided. An approach employing shrinkage priors for partial autocorrelations is then generalised for the multivariate case, using the cumula tive shrinkage and multiplicative gamma process priors to increasingly shrink the partial autocorrelation matrices with increasing lag. Identifying the lag beyond which these ma trices become equal to zero then determines p. Methods for identifying whether a partial autocorrelation matrix is effectively zero are developed. The work is illustrated through application to neural activity data. In particular, a detailed discussion of methods to decompose a VAR into latent processes is provided, which is then used to investigate ultradian rhythms in the brain. Relationships between different regions of the brain are investigated through Granger causality plots. Description: PhD Thesis

2025-01-01T00:00:00Z Whitaker, Samuel http://theses.ncl.ac.uk/jspui/handle/10443/6716 2026-04-09T10:29:25Z 2025-01-01T00:00:00Z

Title: Fast and efficient Bayesian inference for stochastic epidemic models Authors: Whitaker, Samuel Abstract: Epidemics are inherently stochastic in nature, and stochastic kinetic models (SKMs) provide an appropriate way to describe and analyse such phenomena. Given temporal data consisting of, for example, the number of new infections or removals in a given time window, a continuous-time discrete-valued Markov process provides a natural description of the dynamics of each model component, typically taken to be the number of susceptible, exposed, infected or removed individuals. Fitting the resulting SEIR model to time-course data is a challenging task due to the problem of partial observations and, consequently, the intractability of the observed data likelihood. Whilst sampling based inference schemes such as Markov chain Monte Carlo are routinely applied, their computational cost typically restricts analysis to data sets of no more than a few thousand infected cases. Moreover, upon receipt of new data, these schemes typically need to be restarted from scratch. This thesis addresses these issues via two complementary approaches. First, we develop a sequential inference scheme that makes use of a computationally cheap approximation of the most natural Markov process model. Crucially, the resulting model allows a tractable conditional parameter posterior which can be summarised in terms of a set of low dimensional statistics. This is used to rejuvenate parameter samples in conjunction with a novel bridge construct for propagating state trajectories conditional on the next observation of cumulative incidence. The resulting inference framework also allows for stochastic infection and reporting rates. Second, we tackle the intractability of the observed data likelihood in a batch inference setting. We adopt a stochastic differential equation (SDE) representation of the underlying epidemic dynamics by matching the infinitesimal mean and variance to the drift and diffusion coefficients of an Itˆo SDE. We then approximate the SDE to give a tractable Gaussian process, that is, the linear noise approximation (LNA). Unless the observation model linking the LNA to the data is both linear and Gaussian, the observed data likelihood remains intractable. To circumvent this, we marginalise over the latent process by enforcing a Gaussian approximation of the observation model and use a forward filter to efficiently calculate the resulting approximation of the observed data likelihood. The proposed inference methodology is illustrated using both real and synthetic data sets. Where possible, we compare against competing approaches. Description: Ph. D. Thesis.

2025-01-01T00:00:00Z Williams, Patrick John http://theses.ncl.ac.uk/jspui/handle/10443/6713 2026-04-09T08:57:37Z 2025-01-01T00:00:00Z

Title: Development of Full Band Monte Carlo Methods for the Simulation of High Energy Electron Transport in Ultra-Wide Band Gap Semiconductors Authors: Williams, Patrick John Abstract: Silicon is approaching the physical limits of its capabilities in power electronics and so interest turns instead to ultra-wide bandgap semiconductors. This thesis is primarily concerned with understanding charge transport in two ultra-wide bandgap materials, diamond and cubic boron nitride (cBN). The wider band gaps of these materials mean that devices with smaller form fac tors and higher operating efficiencies can be fabricated, while their high thermal conductivities and radiation hardness makes them ideal for harsh environment applications. Due to the nascent stage of research into ultra-wide bandgap semiconductors, theoretical methods are employed to make up for the dearth of experimental results. To this end, density functional theory was used to calculate the ideal crystal structure from which the band structure was calculated and stored on a non-uniform tetrahedral grid that refines itself to minimise error. This was then used to calculate the numerical density of states (DOS) which compared well with what was given in the literature on diamond and cBN. Density functional perturbation theory was also utilised in the calculation of scattering parameters that are generally calculated empirically. A pre-existing Monte Carlo code was modified to enable the simulation of indirect band gap semiconductors with scattering rates determined by the numerically calculated DOS and scattering parameters. These methods were initially applied to silicon to benchmark the process, and the simulation results showed excellent agreement with analytic simulation and experimental results. These methods were then applied to diamond and cBN. The results for diamond compared well with analytic simulation and experimental results given by the literature. Similarly, the results for cBN compared well with analytic simulations from literature. The use of these methods then allows for the simulation of semiconductors at higher energies and for new and emerging materials where experimental results are sparse and empirical methods cannot be employed. Description: Ph. D. Thesis.

2025-01-01T00:00:00Z Macdonald, Ross Glyn http://theses.ncl.ac.uk/jspui/handle/10443/6678 2026-02-12T14:36:39Z 2025-01-01T00:00:00Z

Title: Tailoring light-matter interactions in waveguide networks for computing applications Authors: Macdonald, Ross Glyn Abstract: Computing with electromagnetic waves has, in recent years, emerged as an interesting alternative computing paradigm. This is due to the inherent high-speed (computing at the speed of light in the medium) and the potential for parallelization of electromagnetic wave-based computing systems. Multiple examples of electromagnetic wave-based structures, such as metamaterials, metasurfaces and gratings, have been proposed and demonstrated to perform computing operations. This includes the emulation of digital logic gates and the calculation of operations such as differentiation, integration and convolution. In this PhD thesis, interconnected networks of parallel plate waveguides are exploited to enable high-speed electromagnetic wave-based computing processes. To begin with an introduction to electromagnetism, waveguides and transmission line theory is presented in chapter 1. This is followed in chapter 2 by the outline of an algorithm developed to assist in the characterisation of waveguide networks. In chapter 3, we then explore how waveguide networks may be exploited to emulate conventional computing techniques. Here, we demonstrate how by tailoring the splitting and superposition of transverse electromagnetic pulses at waveguide junctions one can compute the outputs of decision-making processes (i.e., if… then… else… statements). We also exploit the linear superposition of monochromatic waves within waveguide networks to emulate logic operations such as AND and OR logic gates. In chapter 4, transmission line filtering techniques will be exploited to perform 𝑚th order differentiation in the time domain using the Greens function approach. This includes the calculation of fractional derivatives in which 𝑚 may be a positive non-integer value. In chapter 5, it is shown how periodic networks of waveguide-based metatronic circuits may be used to calculate the solutions partial differential equations. This is done with a focus on partial differential equations in the form of the Helmholtz wave equation. Finally, chapter 6 presents a list of the main conclusions of this thesis and potential future work. Description: PhD Thesis

2025-01-01T00:00:00Z