Working at the interface of statistics with applied and computational mathematics

Tagged: Uncertainty Quantification

Yeah! It's a conference in the USA!

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📥  Statistical Applied Mathematics

(Title: with apologies to Miley Cyrus and inspired by "Wierd Al" Yankovic)

In May this year I travelled to the University of Minnesota, Minneapolis for WAVES 2017 (or to give it its full title, the "International Conference on Mathematical and Numerical Aspects of Wave Propagation"). I was accompanied to the wild (mid) west by Elizabeth Arter, Ivan Graham and Euan Spence from the Department of Mathematical Sciences, here in Bath.

So with heady hopes for my first major conference (and my first trip to the USA) I made my way (changing planes in Iceland!) to Minneapolis.

I should explain why I'd gone all the way to Minneapolis for a conference. My research involves waves; acoustic waves, to be precise. I seek to understand the behaviour of sound waves when they move through a random medium, (For example, when sound wave moves through a crowd of people, but you don't know exactly where the people are).

I also design numerical methods for quickly computing properties of these sound waves and I try to prove that these numerical methods work. My research tends to come under the umbrella of `Uncertainty Quantification' -  designing and analysing numerical methods for problems containing randomness.

Having arrived in Minneapolis, had (some) sleep, and been treated to a very large breakfast in the hotel (I never knew pancakes could be that big!), we made our way to the conference venue, the Coffman Memorial Union

The Coffman Memorial Union, our conference venue

Happily, I didn't have to wrestle with the conference timetable on day one - there was a minisymposium all day on "Seismic Waves: Uncertainty Quantification in Imaging/Inversion Across Scales." Most of the talks in the minisymposium came from researchers in seismic imaging. They're interested in reconstructing the rock structure underneath the earth using sound waves.

Seismic imaging is a major motivator for my own research. We're interested in problems surrounding wave propagation and developing fast, accurate algorithms. And yet those in the 'seismic world' have some different concerns to me. I didn't hear any talk of mathematically proving that methods work, rather, they're interested in methods that seem to work well in realistic scenarios. For example, did you know that salt can cause issues for seismic imaging, as it reflects lots of sound waves? It was a valuable experience chatting with them - their interests could well inform the direction of my PhD.

At the end of day one were treated to a public lecture by Michael Berry from the University of Bristol (it's a small world). After this, some people went out for a drink (in the fabulously named Dinkytown area of Minneapolis) but I made my slightly jet lagged way back to the hotel. Why? Because I was talking the next day!

My talk was in the last possible slot on Tuesday evening, before the conference dinner. I wasn't expecting a big crowd! However, there were around 15 people in the room. They heard me speak on "Bounds on the Helmholtz equation in heterogeneous and random media".

A slide from my talk

This is work with my supervisors Ivan Graham and Euan Spence; we have proved that there are certain types of heterogeneous and random media where you can guarantee you'll never experience `resonance'. Resonance is the phenomenon that means an opera singer can shatter a glass, or that you'll find certain notes ring louder than others when you sing in the shower. If you've not experienced this - try it next time you have a shower!

After my talk came the conference dinner, in the impressive yet architecturally quirky McNamara Alumni Centre. The roof is polyhedral and part of the wall is the old entrance to the sports stadium, which leans over the inside space in a mildly worrying fashion.

The wall of the McNamara Alumni Centre - it's an old gate for the football stadium

The banquet was wonderful - we had the fantastic setting, with good food to boot. It was also a fun- and laughter-filled reminder of how multinational the academic community is. At our table of eight, we had five different nationalities represented (British, French, Austrian, American and Mexican).

And it seems that my talk actually made an impact (besides meaning people had to rush to the conference dinner). I was able to have a conversation with one of the audience members later in the week. They work on problems in plasmas, and were interested whether our results could apply to their work.

The following three days of the conference passed in a mixture of talks attended, meals enjoyed and acquaintances made or strengthened. These last two points are interlinked. It's a privilege to be able to go for sushi with a group of people you've met during the week and get to know one of the leaders in your field over lunch!

I have to mention the drinks reception we had in the Weisman Art Museum - we had modern art (I'm still not sure I understand it), views towards downtown Minneapolis over the Mississippi and a jazz trio. However, I don't think we quite appreciated the architecture from the inside!

The Weisman Art Museum

The strengthening of relationships continued until the last evening. You can't help but get to know people better after you've crossed the light rail tracks with them and then spent twenty minutes walking down a largely empty road bordered by abandoned lorry trailers and derelict flour mills in search of a beer hall that one of the group visited once before. To be fair, he'd been there for a conference dinner, knew exactly where he was going, and we had a great evening.

Grain elevators, near our walk on the final evening

And before we knew it, the conference was over, and we were on a flight back home! It was a week filled with waves, maths and mathematicians.I think you'll find me at WAVES 2019, and we might have another blog post title inspired by a song. Can you guess where it's going to be?


Image Credits:

Coffman Memorial Union Minnesota 5.jpg by AlexiusHoratius is licensed under CC BY-SA 3.0, via Wikimedia Commons

Atrium of McNamara Alumni Center, old football stadium gate.jpg by Runner1928 is licensed under CC BY-SA 4.0, via Wikimedia Commons

Weisman Art Museum Minneapolis by tpsdave is licensed under Creative Commons CC0, via Pixabay

Grain Elevators 1 by Jon Platek is licensed under CC BY-SA 3.0, via Wikimedia Commons


My first conferences: A SAMBa story

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📥  Statistical Applied Mathematics

My first year at SAMBa has been quite an eventful one. I can definitely say that SAMBa has delivered on its promise to help me explore different areas of Mathematics. However, this post is not about maths at all (who are we kidding, it probably is), it rather concerns my experience of conference attendance. My very first one was a workshop on big models at the University of Warwick, which incidentally happens to be my undergraduate institution. The reason I went there was to see what the Institute of Data science was up to, and as expected, they were doing things that I was interested in. Statistics, applied mathematics, data science and machine learning.


Swisstech Convention Centre, Lausanne (courtesy of STCC)

My second conference was perhaps the most daunting one. In my quest to know more about uncertainty quantification (UQ), I took up a module with the local expert on it, Prof. Rob Scheichl. This led to the SIAM conference on uncertainty quantification in Lausanne. The venue was breathtaking, to say the least. It was in the Swisstech convention centre at the EPFL. I have never seen an auditorium with that much leg room during the plenary talks. To fund myself, I along with a fellow SAMBAlite, Gianluca, successfully applied for funding from MI-Net. Part of the deal of going there was to further inter university collaboration, and hence the day preceding the conference involved some informal chat with Fabio Nobile's research group. We exchanged ideas and research interests. The rest of the week involved us going to different sessions. They were quite daunting to be honest as most of the speakers were very, very good at what they did. This only increased my desire to actually start a research project and further my knowledge in a specialist area. The thing that I believe was most beneficial for me was to see the use of machine learning in UQ. This contributed to my decision to take up machine learning as my current research project as I could see that UQ would still be an option if I diverted away from it for a bit. I have to say though, my bilinguality helped a lot during the trip. I speak both French and English fluently, coming from a bilingual society (well, we're actually multilingual as most of us speak a third oriental language plus our local dialect, creole. Mauritius FTW right?).


Me, Gianluca and another SAMBa student Matt outside the conference in Lausanne

I went to my next conference after I had chosen my project (which is on automatic damage assessment in x-rays of Psoriatic Arthritis patients). It was a summer school on Gaussian Processes organised by the Machine Learning group at the University of Sheffield. It was the first year where they added the words "and uncertainty quantification" to it. I expected it to be full of computer scientists. To my surprise, the attendees were extremely diverse. There was an analytics team from formula 1; a guy working with Siemens (I think it was Siemens) on wind turbines; and wait for UQ lecturer from Warwick, Tim Sullivan (who is one of the most rigorous applied mathematicians I know) and my final year project supervisor, Mark Girolami. Uncertainty Quantification can mean many things! The summer school had practical sessions and talks from people who are very good at working with Gaussian Processes. One thing I got from the whole thing was that Gaussian Processes are used everywhere, from trying to optimise functions you cannot evaluate, to trying to fix the posteriors you get in Bayesian Inverse Problems. Is there a better alternative? Maybe. The search continues....


Antarctica as modelled using Markov Chain Monte Carlo, a key tool in Uncertainty Quantification (courtesy of the National Science Foundation)

The next conference I went to was very different from my two previous ones. It was actually one on Psoriatic Arthritis (PsA). No maths, just medical researchers and practitioners talking about, well, PsA. I did not get most of what was happening as they were talking about genes and things. They also mentioned "statistics" a lot of times. That was scary. I mean, really scary. When I asked them what kind of tests they were doing the answer was often "I don't know, I just press on a button in stata". It thus seemed to me that medical doctors in general need a better grasp of data science. Hence I tried to get some statistics training into their realm by suggesting we do a little session with consultants undergoing training. This was well received and it is hoped we can do it in the future during one of their training days.

You might be asking yourselves, how did you, a self proclaimed applied mathematician (please don't hate me, I know I did stats as a major) go to a medical workshop? Long story short: I was invited to a meeting in Bath on medical imaging, as I had now started working on this. There I met Prof. Neil McHugh, who works in pharmacology at the University of Bath. I mentioned my desire to know more about the PsA and he suggested I go there.

My English teacher always told me to put a concluding comment in my essays, and this is kind of an essay. The food at non-maths meetings, like the medical imaging one and the PsA one is way better. I had three course warm meals in both of them as opposed to the usual dried out sandwiches that repeat themselves n-times where n is the number of days the meetings stretch out for. Oh, and I'm writing this on a plane to Beijing where I transit before going to teach stats in Mongolia on SAMBa business. This one is for another time!