Mathematics and Statistics
Recent Deposits
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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 spatially-discrete 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 non-volcanic 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 non-volcanic tremor ... -
Hierarchical capture-recapture models
A defining feature of capture-recapture 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 Time-Inhomogeneous 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 time-inhomogeneous 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 mark-recapture 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 model-averaged point estimate is the weighted mean of the estimates from each of the candidate models. ... -
Inference and Characterization of Planar Trajectories
Inference and characterization of planar trajectories have long been the focus of scientific and commercial research. Efficient algorithms for both precise and efficient trajectory reconstruction remain in high demand in ... -
Reflections on ice : scattering of flexural gravity waves by irregularities in Arctic and Antarctic ice sheets
This thesis studies the scattering properties of different types of imperfections in large Arctic and Antarctic ice sheets. Such irregularities include cracks, pressure ridges and both open and refrozen leads. The scattering ... -
Problem solving as an approach to the teaching and learning of mathematics
This thesis presents the findings of a research project, which examined ways in which the participating teachers learned to teach mathematics effectively using a problem-solving approach. The research also examined the ... -
Asymptotics of solutions in evolutionary formulations of the Einstein constraint equations.
Performing a 2+1 split of an initial data set allows one to formulate the Einstein constraint equations as an initial value problem. There are two possible sets of equations that can arise here, the parabolic-hyperbolic ... -
Contemporary wave–ice interaction models
Sea ice is an important indicator and agent of changes in the global climate system. The ice is affected by waves that travel into the Marginal Ice Zone (MIZ) and cause floes to raft, deform and, potentially, fracture. The ... -
Semiparametric dispersal kernels in stochastic spatiotemporal epidemic models
The dispersal kernel plays a fundamental role in stochastic spatiotemporal epidemic models. By quantifying the rate at which an infectious source infects a susceptible individual in terms of their separation distance, the ... -
Modelling strategies to improve genetic evaluation for the New Zealand sheep industry
The question of how best to optimise the accuracy of genetic evaluation for livestock populations has been given new life by the advent of genomics. Therefore we will investigate methods of evaluating and/or improving the ... -
Mass loss due to gravitational waves with a cosmological constant
The theoretical basis for the energy carried away by gravitational waves that an isolated gravitating system emits was first formulated by Hermann Bondi during the 1960s. Recent findings from looking at distant supernovae ...