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Modelling non-linear exposure-disease relationships in a large individual participant meta-analysis allowing for the effects of exposure measurement error
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsMRC Biostatistics Unit, 2012-10-09)
This thesis was motivated by data from the Emerging Risk Factors Collaboration (ERFC), a
large individual participant data (IPD) meta-analysis of risk factors for coronary heart disease(CHD). Cardiovascular disease is the ...
Extremal and probabilistic bootstrap percolation
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2013-11-12)
In this dissertation we consider several extremal and probabilistic problems in bootstrap percolation on various families of graphs, including grids, hypercubes and trees. Bootstrap percolation is one of the simplest ...
Maximum likelihood parameter estimation in time series models using sequential Monte Carlo
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsStatistical LaboratoryDarwin College, 2013-06-11)
Time series models are used to characterise uncertainty in many real-world dynamical phenomena. A time series model typically contains a static variable, called parameter, which parametrizes the joint law of the random ...
Two topics in financial mathematics : Forward utility and consumption functions & Hedging with variance swaps in infinite dimensions
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2010-10)
Financial Mathematics is often presented as being composed of two main branches: one dealing with investment and consumption, with the aim of answering the now ancient question of how people should invest and spend their ...
Automorphisms of free products of groups
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2013-02-05)
The symmetric automorphism group of a free product is a group rich in algebraic structure and with strong links to geometric configuration spaces. In this thesis I describe in detail and for the first time the (co)homology ...
Morita cohomology
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2014-01-07)
This work constructs and compares different kinds of categorified cohomology of a locally contractible topological space X. Fix a commutative ring k of characteristic 0 and also denote by k the differential graded category ...
A 3-manifold group which is not four dimensional linear
(ElsevierJournal of Pure and Applied Algebra, 2014-01-28)
We give examples of closed orientable graph 3-manifolds having a fundamental group which is not a subgroup of GL(4, F) for any field F. This answers a question in the Kirby problem list from 1977 which is credited to the ...
New approaches to modern statistical classification problems
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2015-11-10)
This thesis concerns the development and mathematical analysis of statistical procedures for
classification problems. In supervised classification, the practitioner is presented with the
task of assigning an object to ...
Discussion of ‘An adaptive resampling test for detecting the presence of significant predictors’ by I. W. McKeague and M. Qian
(Taylor & FrancisJournal of the American Statistical Association, 2016-01-15)
We are grateful for the opportunity to discuss this new test, based on marginal screening, of a global null hypothesis in linear models. Marginal screening has become a very popular tool for reducing dimensionality in ...
Stability and bifurcation for the Kuramoto model
(ElsevierJournal de Mathématiques Pures et Appliquées, 2015-11-11)
We study the mean-field limit of the Kuramoto model of globally coupled oscillators. By studying the evolution in Fourier space and understanding the domain of dependence, we show a global stability result. Moreover, we ...