The (developing) website of Jason M. Whyte, PhD.
I’m an Australian applied mathematician with varied analytical and
computational interests, driven by applications.1
Why ‘Synthesis’?
I’m
an inter-disciplinary researcher, always on the lookout for good ideas
from other fields.
My projects have led to new methodologies and software.
People seem easily discouraged by maths. So, I aim to present my work
in talks and posters in a manner that combines information with a
memorable flourish.
Perhaps you saw my poster with a “jigsaw”, or
the one with a 3D-printed error surface?2
Biological modelling: I’ve considered biochemical
systems and human biomarker concentration time series.
The broad
question here is:
Ιf we
can propose a model structure (collection of related models) to
represent a physical system, can we control the system, or predict its
behaviour?
Model
structure analysis: success in modelling may be determined
by the nature of the model structure we use. More data and better
quality data may not remedy a study destined to fail due to undesirable
model properties.
If
estimation of model parameters leads to multiple values that are equally
feasible, what does this mean?
(Hint: problems with
reproducibility of results are possible. If alternative parameter
estimates lead the model structure to produce dissimilar predictions, we
cannot predict system behaviour with confidence.) However, we can
anticipate this type of problem prior to data collection through
interrogating the assumed model structure.
We could call these projects4 “Environmental Data
Science”. Consider the PFAS (per- and poly-fluoroalkyl substances),
which entered into widespread use. Some of these chemicals were then
found to have adverse effects on human and environmental health.
Regulators must now reactively manage this problem.
How can mathematics and statistics
give regulators advance warning of tomorrow’s nightmares?
To gain a sense of the scale of the problem with PFAS “forever
chemicals”: see
this investigation by Tom Perkins, published in The Guardian on
February 24th 2021.