Martin's
Stuff
Research
Teaching
161.200
Personal
Other
Contact
me
m.hazelton
AT massey.ac.nz
tel: +64 6
356 9099 x84642
fax:
+64 6 355 7953
Institute
of Fundamental Sciences
Massey University
Private Bag 11222
Palmerston North 4442
New Zealand


Martin
Hazelton's Personal Webpage
About
Me
Hello and welcome to my webpage. I am Professor of Statistics and
Acting Head of the Institute
of
Fundamental Sciences at Massey
University's Manawatu
campus in Palmerston
North, New
Zealand.
For Current
Massey Students
For information on papers that I currently teach, see the Massey paper
codes under the Teaching heading in the panel on the left. Access to
information on those papers is available throught the Stream learning
environment.
If you are looking for advice on which statistics paper(s) to take,
then feel free to contact
me. If you are considering doing Honours or a PhD in
Statistics and think that you might like to be supervised by me, then
read about my research below.
About
My Research
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. My current
work in this area includes kernel estimation of relative risk functions
in geographical epidemiology, with former PhD student Tilman
Davies (the latter now a senior lecturer at the University of
Otago). Other areas of intetrest 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.
I am currently working with Professor Bill Morgan (Lions
Eye Institute, Western Australia) on some challenging
statistical modelling
problems for ophthalmic data collected from glaucoma patients. I
am also a Principal Investigator in Massey's
Infectious Disease Research Centre (IDReC), where my work includes
modelling patterns of foot and mouth disease in Vietnam with
epidemiologist Prof
Mark Stevenson and former PhD student Kate Richards, and estimation
of spatial risk (as discussed under Smoothing
Methods above).
Spatial Statistics
Through
my interests in smoothing, networks, and geographical epidemiology, I
have an evolving interest in spatial statistics. Much of Tilman
Davies' later work was in this area.
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 20162019. The Principal Investigator
is Tilman
Davies.
Statistical Modelling and Inference in Transportation Science
Transportation
science
generates a huge range of fasinating problems. I'm currently focused on
network tomography (in essence, statistical methods for learning about
high dimensional properies of network traffic flows based on lower
dimensional observations), and modelling and inference for
daytoday dynamic traffic networks, with Professors David
Watling, Giulio
Cantarella, Hong Lo
and Mike Smith. I was
awarded a New Zealand Royal Society Marsden
Fund grant
for 20152019 to work in this area. Iranian PhD student Ahmad
Mahmoodjanlou is working with me on this project. He is cosupervised
by Dr
Katharina Parry, who recently joined Massey as a Lecturer in
Statistics.
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 underdetermined. 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 capturerecapture 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 recently awarded a new Marsden grant, 17MAU037 Lattice polytope samplers: theory, methods and applications (20182020), 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.
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.
I was the recipient of the 2014 Littlejohn Research Award,
the New Zealand Statistical Association's premier research award.
