Maths, business & society: portrait of Estelle Medous

Sponsored by the learned societies Société Française de Statistique (SFDS), Société de Mathématiques Appliquées et Industrielles (SMAI ) and Société Mathématique de France (SMF) , the 2024 thesis prize was awarded at the 13th Forum Entreprises & Mathématiques on Monday October 7, 2024.

• Thesis title: Generalized weight-sharing method and data integration for improving the accuracy of postal traffic estimators in France
• Issuing university : Toulouse Capitole University
• Supervisors: Anne Ruiz-Gazen (Toulouse School of Economics) and Camelia Goga (Université de Franche-Comté)
• Industrial supervisors: Alain Dessertaine and Pauline Puech
• Company: LA POSTE
• Currently a post-doctoral researcher at the Laboratoire de Mathématiques Jean Leray in Nantes; working at the Institut national de l'information géographique et forestière (IGN), in the National Forest Reference Department.

What motivated you to do a thesis linked to the socio-economic world?

I have a bachelor's degree in economics and mathematics, a bachelor's degree in theoretical mathematics and a master's degree in theoretical mathematics. At the end of my master's degree, I knew I wanted to do at least my internship with a link to the socio-economic world, without having too many ideas for the thesis. I got in touch with professors at my economics school to look for internship opportunities. The opportunity came up with the La Poste group, which had an internship to offer: what was supposed to be a thesis preparation internship turned into a thesis.

Can you tell us about your thesis topic?

My thesis is on surveys (a branch of statistics), and more specifically on the generalized weight-sharing method. It's a survey estimation method, in a context where we're targeting a population that's related to our population of interest, i.e. when we can't go and interview that population directly. We go out and observe another population, which is related to our population of interest, we ask them questions and from there we draw conclusions about the population we weren't able to observe. It's a survey method that's quite fashionable at the moment, used by La Poste, and on which there hasn't yet been much theoretical development after the first articles.

Has there been any change in your collaboration with La Poste?

There was indeed an evolution in this collaboration; the department was reorganized following internal directives from the La Poste group. Although I didn't officially change teams, by the end of my thesis I was no longer working with the original team. I wasn't even working on the subject at the end, but on quantum calculations... which didn't end up in the thesis, as it was too far from the subject!

What were the main challenges you encountered during your research?

The Covid19 epidemic was a major challenge. The thesis application was sent in December 2019, and was received six months later instead of the normal three. Another difficulty had more to do with obtaining data. I did a lot of work on data at the start of my thesis, until we needed precise data... which didn't arrive until 6 months before the end of the thesis. So we reversed the percentage of work on theoretical data. The thesis began mainly with data and code creation, and ended mainly with research.

How has your work benefited or will it benefit the socio-economic world in the future?

The method I worked on is being used more and more, because it's so easy to implement. What I've done in my thesis is, on the one hand, a contribution to facilitating implementation, and on the other, it helps to improve precision (but with constraints on implementation).

What advice would you give to young people wishing to direct their mathematical research towards concrete applications?

Choose your supervisors carefully. Don't think that just because you're a PhD student, you have to put up with everything! For me, it went very well: my team listened to me and took good care of me. That's not the case everywhere. In a company, things can get out of hand more easily than in a traditional thesis: you can't let them walk all over you. You're there to do research, not to be an engineer... So it's important to know what you're doing, what you're supposed to be doing, and to keep your distance from the company's demands. Unfortunately, this danger does exist.

Now that you've completed your thesis, what are your next steps?

I'm currently working in the IGN's national forest referencing department. Forest referencing is used for everything to do with carbon footprints and wood quantities. We're working on a public tool that will enable other researchers, notably biologists, to calculate the quantity of a given tree or species in a given territory, for example. As with my thesis, it's a job that mixes theory & application: sometimes I do research to try and understand things and see how we can improve them. Other times, I'll try to dig into the data to understand what's going on in practice.

As a young researcher, how do you see the links between academic mathematics research and the socio-economic world evolving?

I think the two fields are still rather closed to each other. Companies may feel that research is not going to help them with pressing problems, while research tends not to want to talk because companies sometimes have unrealistic obligations in terms of results. Because research takes time. So we need to work more towards common ground.