Martin's
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Research
Teaching
STAT115
STAT310
Personal
Martin
Hazelton's webpage
Contact
me
martin.hazelton
AT otago.ac.nz
tel:
+64 3 4797605
Department
of Mathematics and Statistics
University of Otago
Dunedin
New Zealand


Martin
Hazelton's
Personal Webpage
About
Me
Hello and welcome to my webpage. I am Professor of
Statistics in the Department
of Mathematics and Statistics at the University
of Otago, in beautiful
Dunedin, New Zealand Aotearoa.
For
Current Otago Students
For information on papers that I currently teach, see the
paper codes under the Teaching heading in the panel on the
left.
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. 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
20202020. 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 daytoday dynamic traffic networks.
Statistical Linear Inverse Problems and ZPolytope
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
underdetermined. 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 capturerecapture 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 Zpolytope  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 Zpolytope. This is typically done using a
random walk. The problem then is to construct a random
walk that traverses the Zpolytope 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" (20212024), 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 Zpolytope
sampling, and also likelihoodbased approaches using
saddlepoint approximations (an area in which my
Aucklandbased 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.
Other
Stuff
Awards
I was the recipient of the 2014 Littlejohn
Research Award, the New Zealand Statistical
Association's premier research award.
Editorial
I am EditorinChief of the Australian
and New Zealand Journal of Statistics.
