Professor Martin HazeltonOffice: Science III, room 233
I am Professor of Statistics at the University of Otago. I moved here in 2019, following 13 years as chair of statistics at Massey University in Palmerston North. Prior to that I worked at University of Western Australia, University College London and the University of Oxford.
Statistics Linear Inverse Problems and Polytope Sampling
Network tomography is an example of a statistical linear inverse problem. These are characterized by the linear system y = Ax where y is a vector of observed data (e.g. traffic counts on road segments), x is the variable of principal interest (e.g. traffic volumes between different zones of a network). The configuration matrix A typically has (many) more columns than rows, so that the linear system is under-determined. Other examples with the same structure include (re)sampling entries of a contingency table conditional on various marginal totals, and counts of individual animals in capture-recapture experiments in ecology where misidentification may occur (so that the true counts x differ from the observed counts y).
When the data are counts, the observations y constrain the variables of interest #x# to lie in a lattice polytope - that is, the grid of integer valued coordinates (yellow dots in the figure to the right) within a multidimensional polyhedron. Practical methods of statistical inference (like MCMC) require that we sample vectors x lying in this polytope. This is typically done using a random walk. The problem then is to construct a random walk that traverses the polytope efficiently and yet always remains within its bounds. It turns out that this is a hard problem!
In collaboration with Professor Alan Lee (University of Auckland), Dr Matt Schofield (University of Otago) and Dr Rina Parry (Massey University), I was awarded a Marsden grant, 17-MAU-037 Lattice polytope samplers: theory, methods and applications (2018-2020), by the Royal Society of New Zealand to work on this topic. PhD student Mike McVeagh has joined the team, and I am current advertising for a Postdoctoral Fellow in Statistics to work on computational aspects of the project.
I have long been interested in kernel smoothing problems, and in particular spatially adaptive methods for multivariate data. My current work in this area includes tests for comparing multivariate densities, kernel deconvolution problems and constrained spline smoothing.
Through my interests in smoothing, networks, and geographical epidemiology, I have an evolving interest in spatial statistics. I am Associate Investigator on a New Zealand Royal Society Fast Start Marsden Fund grant entitled "Smoothing and inference for point process data with applications to epidemiology" for 2016-2019. The Principal Investigator is Tilman Davies.
Statistical Theory, Methods and Applications
In addition to these medical areas, I have a general interest in the application of statistical theory and methods. Indeed, one of the great things about working in statistics is that I've had the opportunity to look at a diverse range of intriguing problems from a wide variety of areas, from archaeology, to finance, to zoology.
I am always on the look out for talented postgraduate students to join my research team. At present I am particularly interested in recruiting students to work on polytope sampling and network tomography (see above), and applied projects in vision science (turning video data of the blood vessels on the retina into maps describing damage from diseases like glaucoma).
Ahmad Mahmoodjanlou is working on a PhD modeling the dynamic behaviour of traffic systems. Another PhD student, Jing Liao is investigating campylobacter infections in New Zealand, using genetic data to match human cases with possible sources of infection. Mike McVeagh is also doing a PhD, working in algebraic statistics and related areas. He is seeking to provide theoretical support for the polytope samplers that we are developing. Finally, Matt Schroder is doing a masters looking at strategies in sport betting, particularly american football.
I am Editor-in-Chief of the Australian and New Zealand Journal of Statistics.
Selected recent publications
- Liao, S.-J., Marshall, J., Hazelton, M. L., & French, N. P. (2019). Extending statistical models for source attribution of zoonotic diseases: A study of campylobacteriosis. Journal of the Royal Society Interface, 16(150), 20180534. doi: 10.1098/rsif.2018.0534
- Betz-Stablein, B., Hazelton, M. L., & Morgan, W. H. (2018). Modelling retinal pulsatile blood flow from video data. Statistical Methods in Medical Research, 27(5), 1575-1584. doi: 10.1177/0962280216665504
- Davies, T. M., Marshall, J. C., & Hazelton, M. L. (2018). Tutorial on kernel estimation of continuous spatial and spatiotemporal relative risk. Statistics in Medicine, 37(7), 1191-1221. doi: 10.1002/sim.7577
- Watling, D. P., & Hazelton, M. L. (2018). Asymptotic approximations of transient behaviour for day-to-day traffic models. Transportation Research Part B: Methodological, 118, 90-105. doi: 10.1016/j.trb.2018.10.010
- Davies, T. M., Flynn, C. R., & Hazelton, M. L. (2018). On the utility of asymptotic bandwidth selectors for spatially adaptive kernel density estimation. Statistics & Probability Letters, 138, 75-81. doi: 10.1016/j.spl.2018.02.067