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Professor Martin Hazelton

(MA, D.Phil (Oxon))Martin Hazelton (2022)

Head of Statistics
Director of Studies for 400-level and Honours Statistics
Director of Studies for postgraduate Statistics: Masters and PhD

Office: Science III, room 233
Tel +64 3 479 7605
Email martin.hazelton@otago.ac.nz

About

Martin Hazelton is a statistician with wide-ranging research interests (see below). He has worked previously at the University of Oxford, University College London, the University of Western Australia, and Massey University. Martin is editor-in-chief of the Australian and New Zealand Journal of Statistics.

Teaching responsibilities

teaching responsibilities include:

Research Interests

I have a variety of research interests. These include:

Smoothing Methods

I have long been interested in kernel smoothing problems, and in particular spatially adaptive methods for multivariate data. Other areas of interest include kernel deconvolution problems and constrained spline smoothing.

Biostatistics and Applied Statistics

I have a keen interest in the development and application of statistical methods in medicine, particularly epidemiology and opthalmology.

Spatial Statistics

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 Marsden Fund grant entitled "A new generation of statistical models for spatial point process data" for 2020-2020. The project is led by my former PhD student Tilman Davies, and is in collaboration with Adrian Baddeley (Curtin University, Australia).

Statistical Modelling and Inference in Transportation Science

Transportation science generates a huge range of fascinating problems. I'm currently focused on network tomography (in essence, statistical methods for learning about high dimensional properties of network traffic flows based on lower dimensional observations), and modelling and inference for day-to-day dynamic traffic networks.

Statistical Linear Inverse Problems and Z-Polytope Sampling

Statistical linear inverse problems are characterized by the linear system y = Ax where y is a vector of observed data and x is the variable of principal interest. The configuration matrix A typically has (many) more columns than rows, so that the linear system is under-determined. A classic example is network tomography, where we want to know about traffic flows x on paths through the network but we observe only traffic counts y at various network locations. Other examples with the same structure include (re)sampling entries of a contingency table conditional on various marginal totals, 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), and assessment of items for biosecurity risk under stratified sampling.
When the data are counts, the observations y constrain the variables of interest x to lie in a Z-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 Z-polytope. This is typically done using a random walk. The problem then is to construct a random walk that traverses the Z-polytope efficiently and yet always remains within its bounds. It turns out that this is a hard problem!

I have recently been awarded a Marsden Fund grant as lead researcher on the project "Inference for statistical linear inverse problems: theory and practice" (2021-2024), working with Rachel Fewster, Jesse Goodman (both University of Auckland) and Andrew Robinson (University of Melbourne). This research will examine methods of inference based on Z-polytope sampling, and also likelihood-based approaches using saddlepoint approximations (an area in which my Auckland-based collaborators are expert).

Other Research Topics

In addition to these medical areas, I have a general interest in the application of statistical 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.

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Publications

Baddeley, A., Davies, T. M., Hazelton, M. L., Rakshit, S., & Turner, R. (2022). Fundamental problems in fitting spatial cluster process models. Spatial Statistics. Advance online publication. doi: 10.1016/j.spasta.2022.100709

Hazelton, M. L. (2022). The emergence of stochastic user equilibria in day-to-day traffic models. Transportation Research Part B: Methodological. Advance online publication. doi: 10.1016/j.trb.2022.02.010

Hazelton, M. L., & Davies, T. M. (2022). Pointwise comparison of two multivariate density functions. Scandinavian Journal of Statistics, 49, 1791-1810. doi: 10.1111/sjos.12565

Pirikahu, S., Jones, G., & Hazelton, M. L. (2021). Bayesian credible intervals for population attributable risk from case–control, cohort and cross-sectional studies. Australian & New Zealand Journal of Statistics, 63(4), 639-657. doi: 10.1111/anzs.12352

Hazelton, M. L., & Turner, R. (2021). A Festschrift for Adrian Baddeley. Australian & New Zealand Journal of Statistics, 63(1), 1-5. doi: 10.1111/anzs.12322

Hazelton, M. L. (2016). Kernel smoothing methods. In A. B. Lawson, S. Banerjee, R. P. Haining & M. D. Ugarte (Eds.), Handbook of spatial epidemiology. (pp. 195-207). Boca Raton, FL: CRC Press.

Chapter in Book - Research

Hazelton, M. L. (2015). Nonparametric regression. In J. D. Wright (Ed.), International encyclopedia of the social & behavioral sciences. (2nd ed.) (pp. 867-877). Elsevier. doi: 10.1016/B978-0-08-097086-8.42124-0

Chapter in Book - Research

Hazelton, M. L. (2010). Univariate linear regression. In P. Peterson, E. Baker & B. McGaw (Eds.), International encyclopedia of education. (3rd ed.) (pp. 482-488). Elsevier. doi: 10.1016/B978-0-08-044894-7.01373-7

Chapter in Book - Research

Baddeley, A., Davies, T. M., Hazelton, M. L., Rakshit, S., & Turner, R. (2022). Fundamental problems in fitting spatial cluster process models. Spatial Statistics. Advance online publication. doi: 10.1016/j.spasta.2022.100709

Journal - Research Article

Hazelton, M. L. (2022). The emergence of stochastic user equilibria in day-to-day traffic models. Transportation Research Part B: Methodological. Advance online publication. doi: 10.1016/j.trb.2022.02.010

Journal - Research Article

Hazelton, M. L., & Davies, T. M. (2022). Pointwise comparison of two multivariate density functions. Scandinavian Journal of Statistics, 49, 1791-1810. doi: 10.1111/sjos.12565

Journal - Research Article

Hazelton, M. L., McVeagh, M. R., & van Brunt, B. (2021). Geometrically aware dynamic Markov bases for statistical linear inverse problems. Biometrika, 108(3), 609-626. doi: 10.1093/biomet/asaa083

Journal - Research Article

Pirikahu, S., Jones, G., & Hazelton, M. L. (2021). Bayesian credible intervals for population attributable risk from case–control, cohort and cross-sectional studies. Australian & New Zealand Journal of Statistics, 63(4), 639-657. doi: 10.1111/anzs.12352

Journal - Research Article

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

Journal - Research Article

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

Journal - Research Article

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

Journal - Research Article

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

Journal - Research Article

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

Journal - Research Article

Hazelton, M. L. (2017). Testing for changes in spatial relative risk. Statistics in Medicine, 36(17), 2735-2749. doi: 10.1002/sim.7306

Journal - Research Article

Hazelton, M. L., & Bilton, T. P. (2017). Polytope samplers for network tomography. Australian & New Zealand Journal of Statistics, 59(4), 495-611. doi: 10.1111/anzs.12216

Journal - Research Article

Davies, T. M., Jones, K., & Hazelton, M. L. (2016). Symmetric adaptive smoothing regimens for estimation of the spatial relative risk function. Computational Statistics & Data Analysis, 101, 12-28. doi: 10.1016/j.csda.2016.02.008

Journal - Research Article

Hazelton, M. L., & Cox, M. P. (2016). Bandwidth selection for kernel log-density estimation. Computational Statistics & Data Analysis, 103, 56-67. doi: 10.1016/j.csda.2016.05.003

Journal - Research Article

Hazelton, M. L., & Parry, K. (2016). Statistical methods for comparison of day-to-day traffic models. Transportation Research Part B: Methodological, 92(Part A), 22-34. doi: 10.1016/j.trb.2015.08.005

Journal - Research Article

Lam, J., Chan, G., Morgan, W. H., Hazelton, M., Betz-Stablein, B., Cringle, S. J., & Yu, D. Y. (2016). Structural characteristics of the optic nerve head influencing human retinal venous pulsations. Experimental Eye Research, 145, 341-346. doi: 10.1016/j.exer.2016.02.003

Journal - Research Article

Morgan, W. H., Hazelton, M. L., & Yu, D.-Y. (2016). Retinal venous pulsation: Expanding our understanding and use of this enigmatic phenomenon. Progress in Retinal & Eye Research, 55, 82-107. doi: 10.1016/j.preteyeres.2016.06.003

Journal - Research Article

Morgan, W. H., House, P. H., Hazelton, M. L., Betz-Stablein, B. D., Chauhan, B. C., Viswanathan, A., & Yu, D.-Y. (2016). Intraocular pressure reduction is associated with reduced venous pulsation pressure. PLoS ONE, 11(1), e0147915. doi: 10.1371/journal.pone.0147915

Journal - Research Article

Parry, K., Watling, D. P., & Hazelton, M. L. (2016). A new class of doubly stochastic day-to-day dynamic traffic assignment models. EURO Journal on Transportation & Logistics, 5(1), 5-23. doi: 10.1007/s13676-013-0037-x

Journal - Research Article

Pirikahu, S., Jones, G., Hazelton, M. L., & Heuer, C. (2016). Bayesian methods of confidence interval construction for the population attributable risk from cross-sectional studies. Statistics in Medicine, 35(18), 3117-3130. doi: 10.1002/sim.6870

Journal - Research Article

Guillot, E. G., Hazelton, M. L., Karafet, T. M., Lansing, J. S., Sudoyo, H., & Cox, M. P. (2015). Relaxed observance of traditional marriage rules allows social connectivity without loss of genetic diversity. Molecular Biology & Evolution, 32(9), 2254-2262. doi: 10.1093/molbev/msv102

Journal - Research Article

Hazelton, M. L. (2015). Network tomography for integer-valued traffic. Annals of Applied Statistics, 9(1), 474-506. doi: 10.1214/15-AOAS805

Journal - Research Article

Morgan, W. H., Abdul-Rahman, A., Yu, D.-Y., Hazelton, M. L., Betz-Stablein, B., & Lind, C. R. P. (2015). Objective detection of retinal vessel pulsation. PLoS ONE, 10(2), e0116475. doi: 10.1371/journal.pone.0116475

Journal - Research Article

Stephenson, T., Hazelton, M., Kupsta, M., Lepore, J., Andreassen, E. J., Hoff, A., … Mitlin, D. (2015). Thiophene mitigates high temperature fouling of metal surfaces in oil refining. Fuel, 139, 411-424. doi: 10.1016/j.fuel.2014.08.049

Journal - Research Article

Bilton, P. A., da Campo, R., Nikzad, R., Hazelton, M., & Derrick, P. J. (2014). Interactions between naphthenic acids: Dependence on molecular structure revealed through statistical analysis of ultra-high-resolution electrospray mass spectra. European Journal of Mass Spectrometry, 20(3), 221-231. doi: 10.1255/ejms.1275

Journal - Research Article

Fernando, W. T. P. S., & Hazelton, M. L. (2014). Generalizing the spatial relative risk function. Spatial & Spatio-temporal Epidemiology, 8, 1-10. doi: 10.1016/j.sste.2013.12.002

Journal - Research Article

Fernando, W. T. P. S., Ganesalingam, S., & Hazelton, M. L. (2014). A comparison of estimators of the geographical relative risk function. Journal of Statistical Computation & Simulation, 84(7), 1471-1485. doi: 10.1080/00949655.2012.748055

Journal - Research Article

Morgan, W. H., Hazelton, M. L., Betz-Stablein, B. D., Yu, D.-Y., Lind, C. R. P., Ravichandran, V., & House, P. H. (2014). Photoplethysmographic measurement of various retinal vascular pulsation parameters and measurement of the venous phase delay. Investigative Ophthalmology & Visual Science, 55(9), 5998-6006. doi: 10.1167/iovs.14-15104

Journal - Research Article

Richards, K. K., Hazelton, M. L., Stevenson, M. A., Lockhart, C. Y., Pinto, J., & Nguyen, L. (2014). Using exceedance probabilities to detect anomalies in routinely recorded animal health data, with particular reference to foot-and-mouth disease in Viet Nam. Spatial & Spatio-temporal Epidemiology, 11, 125-133. doi: 10.1016/j.sste.2014.08.002

Journal - Research Article

Shao, H., Lam, W. H. K., Sumalee, A., Chen, A., & Hazelton, M. L. (2014). Estimation of mean and covariance of peak hour origin–destination demands from day-to-day traffic counts. Transportation Research Part B: Methodological, 68, 52-75. doi: 10.1016/j.trb.2014.06.002

Journal - Research Article

Betz-Stablein, B. D., Morgan, W. H., House, P. H., & Hazelton, M. L. (2013). Spatial modeling of visual field data for assessing glaucoma progression. Investigative Ophthalmology & Visual Science, 54(2), 1544-1553. doi: 10.1167/iovs.12-11226

Journal - Research Article

Davies, T. M., & Hazelton, M. L. (2013). Assessing minimum contrast parameter estimation for spatial and spatiotemporal log-Gaussian Cox processes. Statistica Neerlandica, 67(4), 355-389. doi: 10.1111/stan.12011

Journal - Research Article

Parry, K., & Hazelton, M. L. (2013). Bayesian inference for day-to-day dynamic traffic models. Transportation Research Part B: Methodological, 50, 104-115. doi: 10.1016/j.trb.2013.01.003

Journal - Research Article

Parry, K., & Hazelton, M. L. (2012). Estimation of origin–destination matrices from link counts and sporadic routing data. Transportation Research Part B: Methodological, 46(1), 175-188. doi: 10.1016/j.trb.2011.09.009

Journal - Research Article

Davies, T. M., Hazelton, M. L., & Marshall, J. C. (2011). sparr: Analyzing spatial relative risk using fixed and adaptive kernel density estimation in R. Journal of Statistical Software, 39(1). Retrieved from http://www.jstatsoft.org/v39/i01/paper

Journal - Research Article

Hazelton, M. L. (2011). Assessing log-concavity of multivariate densities. Statistics & Probability Letters, 81(1), 121-125. doi: 10.1016/j.spl.2010.10.001

Journal - Research Article

Hazelton, M. L., & Turlach, B. A. (2011). Semiparametric regression with shape-constrained penalized splines. Computational Statistics & Data Analysis, 55(10), 2871-2879. doi: 10.1016/j.csda.2011.04.018

Journal - Research Article

Sanson, R. L., Harvey, N., Garner, M. G., Stevenson, M. A., Davies, T. M., Hazelton, M. L., … Owen, K. (2011). Foot and mouth disease model verification and 'relative validation' through a formal model comparison. Revue Scientifique et Technique, 30(2), 527-540. doi: 10.20506/rst.30.2.2051

Journal - Research Article

Davies, T. M., & Hazelton, M. L. (2010). Adaptive kernel estimation of spatial relative risk. Statistics in Medicine, 29(23), 2423-2437. doi: 10.1002/sim.3995

Journal - Research Article

Hazelton, M. L. (2010). Bayesian inference for network-based models with a linear inverse structure. Transportation Research Part B: Methodological, 44(5), 674-685. doi: 10.1016/j.trb.2010.01.006

Journal - Research Article

Hazelton, M. L. (2010). Statistical inference for transit system origin-destination matrices. Technometrics, 52(2), 221-230. doi: 10.1198/TECH.2010.09021

Journal - Research Article

Hazelton, M. L., & Turlach, B. A. (2010). Semiparametric density deconvolution. Scandinavian Journal of Statistics, 37(1), 91-108. doi: 10.1111/j.1467-9469.2009.00669.x

Journal - Research Article

Marshall, J. C., & Hazelton, M. L. (2010). Boundary kernels for adaptive density estimators on regions with irregular boundaries. Journal of Multivariate Analysis, 101(4), 949-963. doi: 10.1016/j.jmva.2009.09.003

Journal - Research Article

Sadler, R. J., Hazelton, M., Boer, M. M., & Grierson, P. F. (2010). Deriving state-and-transition models from an image series of grassland pattern dynamics. Ecological Modelling, 221(3), 433-444. doi: 10.1016/j.ecolmodel.2009.10.027

Journal - Research Article

Hazelton, M. L., & Davies, T. M. (2009). Inference based on kernel estimates of the relative risk function in geographical epidemiology. Biometrical Journal, 51(1), 98-109. doi: 10.1002/bimj.200810495

Journal - Research Article

Hazelton, M. L., & Marshall, J. C. (2009). Linear boundary kernels for bivariate density estimation. Statistics & Probability Letters, 79(8), 999-1003. doi: 10.1016/j.spl.2008.12.003

Journal - Research Article

Hazelton, M. L., & Turlach, B. A. (2009). Nonparametric density deconvolution by weighted kernel estimators. Statistics & Computing, 19(3), 217-228. doi: 10.1007/s11222-008-9086-7

Journal - Research Article

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