Mathematics and Statistics
Recent Deposits

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. ... 
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 problemsolving 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 parabolichyperbolic ... 
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 ... 
The structure of GCR and CCR groupoid C*algebras
We remove the assumptions of amenability in two theorems of Clark about C*algebras of locally compact groupoids. The first result is that if the groupoid C*algebra is GCR, or equivalently then the groupoid's orbits are ... 
Inverse problems in evolutionary biology
In this thesis, we explore three techniques which could be used to increase the efficiency of analyses in evolutionary genetics while still producing reasonably accurate results. The first of these methods improves the ... 
Modeling Continuous Time Series With Many Zeros
Earthquake activity is generally modeled using point processes as earthquake events usually occur at random times and locations. Recent studies have found it mathematically challenging and computationally complex to ... 
Analogues of Leavitt path algebras for higherrank graphs
Directed graphs and their higherrank analogues provide an intuitive framework to study a class of C*algebras which we call graph algebras. The theory of graph algebras has been developed by a number of researchers and ... 
C*algebras generated by semigroups of partial isometries
This thesis examines the C*algebras associated to semigroups of partial isometries. There are many interesting examples of C*algebras generated by families of partial isometries, for example the C*algebras associated ... 
The behaviour of sea ice in ocean waves
The entry of ocean waves from the open sea into pack ice is a feature of the marginal ice zone which has important consequences for navigation and the construction of offshore structures in iceinfested seas. In turn it ... 
Towards a Fast Bayesian Climate Reconstruction
To understand global climate prior to the availability of widespread instrumental data, we need to reconstruct temperatures using natural proxies such as tree rings. For reconstructions of a temperature field with multiple ...