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Professor Marriott's research activity is split fairly evenly between theoretical and applied work.
One aspect of his work is in the area of theoretical mathematical statistics and looks at ways of applying ideas from geometry (often, but not exclusively, differential geometry) to statistical theory. His early work in this area concentrated on the idea of a preferred point geometry. This form of geometry seems to be the most natural framework suitable for applications in statistics. These earlier geometric ideas found fruitful applications in econometrics. More recent work is on the geometry of mixture models. He introduced the idea of a local mixture that has extremely attractive statistical properties. This form of mixture geometry has applications in areas such as measurement error modelling, modelling censored data, influence analysis, and dispersion modelling. Other work includes global analysis of statistical problems, and lifetime data analysis.
In the area of applied stochastic modelling, Professor Marriott has worked on a broad range of applied projects across many subject areas; these include physics, linguistics, and medical statistics. Currently he is actively working in a number of areas including Rutherford backscattering in material science where it is required to infer the structure of a sample of material (for example its elemental depth profile) from the spectrum generated by the backscatter of a stream of alpha-particles. While he was at Duke University he started working with Michael Lavine and a team of neuro-scientists on understanding data from neuron-firing experiments.
Professor Marriott joined Statistics and Actuarial Science in 2004 and is currently the Department Chair. After graduating in 1989, Professor Marriott worked in statistics departments in the UK (Surrey University), Singapore (the National University of Singapore), and the US (Duke University). He arrived at the University of Waterloo in 2004. He has done statistical consulting in a number of medical and biological science areas, as well as in those areas mentioned above which form part of his methodological research.