Mathematics and Statistics
Recent Deposits

Modelling functional data with Bayesian workflow
In many cases of statistical interest, observations can be viewed as measurements taken at different times of an underlying unknown function. In healthrelated fields, such measurements are crucial to the health and ... 
Hidden Markov modeling of sparse time series from nonvolcanic tremor observations
Tremor activity has been recently detected in various tectonic areas world wide and is spatially segmented and temporally recurrent. We design a type of hidden Markov models to investigate this phenomenon, where each state ... 
Development of integrated distance sampling models
Distance sampling methods are used to estimate abundance of biological populations. A set of randomlyplaced lines or points are traversed and the distances to detected objects are recorded; these distances are used to ... 
Two applications of the Cauchy problem in general relativity
The Cauchy problem plays an important role in both analytical and numerical studies of the Einstein field equations. Here we discuss two particular applications of the Cauchy problem within the framework of General Relativity. ... 
Profile decomposition for the KleinGordon equation
We use refined Strichartz estimates to prove profile decompositions for the wave equation in ̇H1/2(Rd) and for the KleinGordon equation in H1/2(Rd); the former is an alternative proof of a result originally obtained by ... 
Constructive Arrows: An Introduction to Categories, Toposes and Logic
Category theory, especially topos theory, admits a new perspective on the study of logic and mathematical foundations. In this dissertation, we provide an introduction to the development of logic in a topos, and show why ... 
Approximating Solutions to ConvectionDiffusion Equations by Tensor Train Decompositions
A finite volume method for solving general timehomogeneous convectiondiffusion equations with zero source term is presented. Computational efficiency of the method is improved by performing linear algebra in the tensor ... 
Data Selection Strategies for Bayesian Analysis with Filtering of Genetic Data
The aim of this thesis is to look into data selection strategies for selecting data to be used for Bayesian analysis of genotyping by sequencing (GBS) data. Each selection of data leads to a different distribution on the ... 
Predicting the past: Mathematical models and numerical methods in molecular phylogenetics
Molecular phylogenetics is the study of phylogenies and processes of evolution by the analyses of DNA or amino acid sequence data. In this thesis we describe a computationally efficient Bayesian methodology for ... 
Modelling Invasive Species using Markov Jump Processes
Predicting the dispersal of an invasive species over a heterogeneous region is a difficult yet important task, since these predictions can inform biosecurity efforts and threatened industries. A spatiallydiscrete population ... 
Ornstein Uhlenbeck Jump Models of Evolution
In this thesis we explore models of continuous trait evolution which allow for sudden changes in trait values. Starting with the Ornstein Uhlenbeck process, we introduce two new models based on combinations of the Ornstein ... 
Model selection and model checking for hidden Markov models applied to nonvolcanic tremor data
Hidden Markov models (HMMs) are commonly used to model time series data and are now widely applied in many fields. In the field of seismology, HMMs have recently been applied to data collected from nonvolcanic tremor ... 
Hierarchical capturerecapture models
A defining feature of capturerecapture is missing data due to imperfect detection of individuals. The standard approach used to deal with the missing data is to integrate (or sum) over all the possible unknown values. The ... 
Identifying the Recurrence Patterns of Nonvolcanic Tremors Using a 2‐D Hidden Markov Model With Extra Zeros
Nonvolcanic tremor activity has been observed in many places worldwide. In some regions, their activity was observed to accompany slow slip events. Before examining whether and how nonvolcanic tremor activity is related ... 
Characterisation of Spherical Splits
We investigate the properties of collections of linear bipartitions of points embedded into $\R^3$, which we call collections of affine splits. Our main concern is characterising the collections generated when the points ... 
Hidden Markov Models for TimeInhomogeneous and Incompletely Observed Point Processes
Many point processes such as earthquakes or volcanic eruptions usually have incomplete records with the degree of incompleteness varying over time. Consequently, hazard estimation from such timeinhomogeneous incomplete ... 
Numerical scalar curvature deformation and a gluing construction
In this work a new numerical technique to prepare Cauchy data for the initial value problem (IVP) formulation of Einstein's field equations (EFE) is presented. Our method is directly inspired by the exterior asymptotic ... 
Estimating Overdispersion in Sparse Multinomial Data
The phenomenon of overdispersion arises when the data are more variable than we expect from the ﬁtted model. This issue often arises when ﬁtting a Poisson or a binomial model. When overdispersion is present, ignoring it ... 
Properties of Gibbs samplers for inference in genetic markrecapture models
The aim of this thesis is to study the convergence properties of specific MCMC algorithms for sampling from a posterior distribution. The model considered incorporates the uncertainty in the assignment of a legitimate ... 
Focussed Model Averaging in Generalised Linear Models
Model averaging is often used to allow for uncertainty in the model selection process. In the frequentist setting, a modelaveraged point estimate is the weighted mean of the estimates from each of the candidate models. ...