On 24th September 2019 the New South Wales branch gathered on the
campus Macquarie University in north-western Sydney. Members of
the council with offices in the inner suburbs had their Opal cards
and transport apps kept busy in the race to out to North Ryde for
their pre-talk monthly meeting. The writer of this article was declared
the winner, making it door to door in just 45 minutes.
After some high quality hors d'oeuvres the audience sat down to
listen to Dr Pierre Lafaye de Micheaux of the School of Mathematics
and Statistics, University of New South Wales, deliver a presentation
titled "A notion of depth for curve data", which uses ideas from
Princeton statistician John Tukey from the 1970s concerning, for
example, half-space depth for point clouds.
Pierre's research in this area is motivated by data from the
Older Australian Twins Study. There is strong evidence that the
quality of brain fibres impacts quality of life and, therefore,
high quality analyses of brain fibre data is important. The
data are curves in three dimensions so Pierre has had to
extend data depth ideas to this setting. The presenter made
excellent use of three dimensional graphics to visualise
the data and explain the depth concepts.
Another key idea was the concept of parametrised curves
and this involved some elegant geometry-type mathematics
including, of course, the Frechet metric.
After a theoretical exposition Pierre demonstrated his
breadth as a statistician by telling everyone about his
co-authored R package named curveDepth.
Apart from data from the Older Australian Twins Study the
methodology was applied to cyclone paths in the Gulf of Mexico.
The new methodology leads to better detection of outlier cyclones
and better confidence regarding regions at risk. For the brain
fibre applications, an upcoming challenge is to go from data
on 68 brains to 20,000 brains.
University of Technology Sydney