“I like the Bayesian approach because I find it natural and it has this kind of internal coherence that makes it very appealing”: An interview with Judith Rousseau

Judith Rousseau is a Professor of Statistics at CEREMADE, Université Paris Dauphine. Her research interests focus on Bayesian statistics and the interraction between Bayesian and frequentist approaches and it is this research that led to her becoming the first winner of the Bernoulli Society’s Ethel Newbold Prize in 2015. Her pape

Last year, the Society approved the establishment of the prize for excellence in statistics, which will now be awarded every 2 years. The name of the prize recognizes a historically important role of women in statistics and is supported by Wiley. It can be awarded to a recipient of any gender who is an outstanding statistical scientist for a body of work that represents excellence in research in mathematical statistics and/or excellence in research that links developments in a substantive field to new advances in statistics.

Ethel Newbold was an English epidemiologist and statistician. She was educated at Tunbridge Wells High School, and Newnham College, Cambridge. She first taught at Godolphin School, Salisbury. Her move to statistics was induced by her work during the First World War in the Ministry of Munitions. She studied for a M.Sc. in the University of London, which she received in 1926, and was awarded a Doctorate in 1929. She became a member of the Medical Research Council in 1921, working on medical and industrial studies.

Professor Rousseau is also Associate Editor for a number of journals, including Annals of Statistics, Bernoulli, ANZJS and stats, she is Secretary of the O’Bayes section of ISBA and Programme secretary of the IMS. Alison Oliver talks to Professor Rousseau about her career and award winning research.

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1. What was it that first introduced you to statistics as a discipline and what was it that led you to pursue a career in the field?

It was quite by chance really, in France we have this system of Grandes Ecoles, I studied at ENSAE which is one of them and specialized in statistics and economy. Before as an undergraduate, I studied pure maths. I discovered probability which I had never heard of before and I thought ‘Wow’. One year later, I was introduced to statistics and somehow I was more into statistics than probability. From a research point of view, I found it more exciting because of all the interactions it has with other fields.

2. You teach at Université Paris Dauphine. Does your teaching and research motivate each other? For example, do you get ideas from your research that you then incorporate into your teaching?

Yes, it’s more in the latter direction you mention. We teach courses that closely affiliate with our research so I teach MA students a course in Bayesian nonparametric statistics which is the domain of my research.

Whenever you teach statistics, there is always something that relates to new things and you are always trying to make it interesting for the students. Even when you are talking about basic statistics, you try to connect to today’s fascinating challenges to help give a few pointers along the way.

3. Your research interests focus on Bayesian statistics and the interaction between Bayesian and frequentist approaches. What are you working on at the moment?

Most of my research is related to theory. I like the Bayesian approach because I find it natural and it has this kind of internal coherence that makes it very appealing. I find it also important to make sure there are good frequentist properties and so that is why I have always been playing in both worlds and trying to understand these properties via various approaches. Another reason why I enjoy working in this interplay is the fact that it sheds light on what you are doing in the Bayesian world. By looking at the frequentist properties of Bayesian procedures, you have a better understanding of them, especially in complex models where it is very hard to understand what the prior is doing as it acts in a complex space. Studying the asymptotic properties sheds light on the behaviour of the approach – how the prior acts with respect to the likelihood and how both are acting together, which gives you a better understanding overall in what you are doing.

4. Congratulations on winning the Ethel Newbold Prize, which recognizes a historically important role of women in statistics and is supported by Wiley. Please could you tell us about the particular research that won this award?

It was a great surprise to me. I think at about this period some people were highlighting particular aspects of my research on the Bernstein-von Mises theorem. With some co-authors, we have been studying the asymptotic shape of the posterior distribution of a finite dimensional parameter of interest in a model that contains an infinite dimensional parameter. Typically, when you have the Bernstein von Mises property, the posterior distribution is asymptotically Gaussian with a well behaved mean and variance. It is a useful property because then, the Bayesian measures of uncertainty are also frequentist measures of uncertainty and so you are winning in both worlds – a Bayesian approach that has really good frequentist properties. This is a well known result in finite dimensional models.

We were interested in trying to have the same kind of properties but in a infinite dimensional world but looking at finite dimensional aspect of it, i.e. finite dimensional resume or functional of your parameters. We first studied linear functionals of the density, sch as the cumulative distribution function. For instance we showed that for infinite-dimensional exponential families, under quite general assumptions, the asymptotic posterior distribution of the linear functional can be either Gaussian or a mixture of Gaussian distributions with different centering points. This illustrates the positive, but also the negative, phenomena that can occur in the study of Bernstein–von Mises results.

These kind of results require a rather refined control on infinite dimensional integrals, which makes them non trivial. We were one of the firsts to develop a general methodology to prove such results, this is why some thought it was an interesting result. It is not completely clear however how very general our methodology is. It opened a door but I think there is still much more to be done on the subject.

5. What is the best book on statistics that you have ever read?

There are so many that have been influential in my career but if I were to decide on two, one is The Bayesian Choice by Christian Robert because it was for me a starting point to try Bayesian statistics. The other is Asymptotic Statistics by A. W. Van de Vaart.

6. What do you see as the greatest challenge facing the profession of statistics?

Many say that data science is becoming the domain and you have to ensure that statistics is not kicked out of it. We have to make sure that data scientists not only do rational research but also work on measures of uncertainty. It is not easy because typically these models are very complicated. The techniques are high-dimensional in every direction. I am working in a more traditional way admittedly but we still need to ensure that we are part of the game.

7. Who are the people who have been influential in your career?

Certainly my PhD advisor when I was a student – Christian Robert. He was the one who introduced me to Bayesian statistics. Then, there are others who have been influential through the papers that they have written, such as J.K. Ghosh, Ghosal and van der Vaart who opened the field of frequentist properties for Bayesian nonparametrics. Jim Berger for the openess of his understanding of the relation between Bayesian and frequentist approaches and I have really followed his work and his approach mirrors mine.

Those who have been more influential from a human point of view include Sonia Petrone and Kerrie Mengersen and I consider them as role models.

8. If you had not got into the field of statistics, what do you think you would have done?

This is hard to say. As an undergraduate student I wanted to do pure maths, so who knows what I would have chosen if I hadn’t studied at ENSAE. Research for sure, however.

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