Features: Faculty Insights

## After several years on secondment as Chief Scientific Advisor to the Home Office, Sir John Aston has returned to research full time as the Harding Professor of Statistics in Public Life in the Department of Pure Mathematics and Mathematical Statistics. In June 2021 he was knighted in the Queen's Birthday Honours in recognition of his services to statistics and public policymaking.

"It was very surprising, rather shocking, but very nice!" says Aston. He hopes that as well as recognising how useful statistics is in so many different disciplines, particularly in public policy, it also is recognition that the way mathematicians think is useful. "Thinking about how to abstract something and then put the answer back into the place it came from is a really useful skill."

### Different backyards

"I'm really interested in how you can use statistics to gain insight into lots of different areas," says Aston. The famous statistician John Tukey (Aston's academic great-grandfather - his supervisor's supervisor's supervisor) said that the best thing about being a statistician is you get to play in everybody else's backyard. "That's the thing I really like. I get to look at medical imaging data one day, look at linguistics and understand how languages evolve another day, and look at how the economy works another day. All these things have a lot of commonality in the types of statistics and mathematical models you can use."

Aston works in functional data analysis – the statistics of curves and surfaces. We often think of statistics as numbers – your height or your weight – or perhaps as collections of numbers, such as how height and weight vary together.

If you were monitoring, say, a child's height as they grow from age 0 to 18, you could take as many measurements as you like: once a year, once a day, once a second. "I'm interested in the setting where you can have as many measurements as you want, infinitely many measurements." Such collections of potentially infinitely many measurements can be seen as a curve, or if you are collecting data in multiple dimensions (such as measuring a feature of the brain at every location), these collections form a surface.

Aston often uses something called principal component analysis to look for the underlying patterns in variation of the data, using well known mathematical techniques such as eigenvalues and eigenvectors that can be generalised to more complicated settings. (You can read an example of the use of principal component analysis in analysing image data here.)

"Those [techniques] can be used when I'm looking for a pattern in brain images, for example if I want to understand what factors are involved in changing brain shapes then I could pick up those patterns using the principal components," says Aston. He uses the same techniques to look at the data from sound recordings: "I can look at which patterns remain similar over time and which vary. And that gives me an idea of how languages evolve." Aston is motivated by the mathematics behind these techniques and also by applications to different areas.

### The ultimate backyard

From 2017 to 2020 Aston was seconded to work as Chief Scientific Advisor (CSA) to the Home Office. "It was a really enjoyable job and I got to look at some incredible things. Everything from Salisbury [the poisoning of Sergei and Yulia Skripal in 2018] all the way through to COVID. So the last year of my time in the Home Office was exceptionally busy."

He was responsible for making sure the Home Secretary, other ministers, the permanent secretary and other officials, got access to the best science advice, so that they could take that science advice into account when they were making policy decisions. He was also responsible for the hundreds of people working on science, statistics, economics, operations research and strategy in the Home Office. "Part of my role was getting them the best access to the science outside and that they felt like they were a part of a community of people working on these things."

I like to think that the things I'm doing help answer other people’s questions as well... I get to do the statistics which is the bit I like, but then I also get to see that they can then understand what they are doing and that gives me a real kick. John Aston

"In some sense that was the ultimate backyard as I got to look into all sorts of science, not just statistics," says Aston. The Home Office is responsible for crime, policing, borders and immigration, national security and counterterrorism. These areas draw on science and analysis from physics, chemistry and biology, through data science all the way to social sciences and economics. "Obviously I don't really know a lot about those subjects so it was about bringing together people who were the real experts in these areas and making sure that [information] was flowing into the policy process."

Aston saw a lot of his role as being a translator – helping turn academic material from all these different areas into something that was easily accessible to those who didn't have a scientific background – which drew on his many years of working with people from many different disciplines.

### Bridging two worlds

During his time as Chief Scientific Advisor, Aston continued to work with students in the Faculty. "I was very fortunate I had some really excellent PhD and postdoc students during the time I was at the Home Office," says Aston. "It was a joy to be able to talk to them about research that was different from what was going on in the Home Office. Government is quite immediate and research in universities often takes a longer view. Having those two worlds was nice."

Aston has now returned to working full time in the Faculty as the Harding Professor of Statistics in Public Life. Previously this chair was held by David Spiegelhalter, and thanks to the generosity of David and Claudia Harding it has now been updated to reflect Aston's work. "David was very much focused on public understanding of uncertainty, and [the chair is now] slightly more focussed towards government, about how statistics and other quantitative evidence can be used in public policy and public life."

"One of the nice things about working as a CSA is that you get to work with other CSAs across all government [departments]. I got to see how science is used throughout. Coming back to the Harding chair here in Cambridge allows me to now think about how I can help people in academia get their work into government. There are some amazing methods being developed that should be championed as they could really help the government."