“On the shoulders of…” Luc Bauwens (UCLouvain), by Arnaud Dufays (EDHEC)

* This title is inspired by a phrase used and adapted over the centuries by many intellectuals, and refers more directly in France to Jean-Claude Ameisen's famous France Inter programme, Sur les épaules de Darwin. For 12 years, this tireless disseminator of knowledge took listeners on a journey ‘through research, culture and social life’, and we invite you to (re)discover the 600 episodes in podcast form. In all modesty, we would like to contribute to this epistemological approach by giving our professors the opportunity to tell us why and how leading figures in research and the economic world have influenced their careers. We invite you to read the previous issues: “On the shoulders of…” Joanne Martin (Stanford), by Youcef Bousalham & “On the shoulders of…” Marc Bloch (1886-1944), by Ludovic Cailluet.

Luc Bauwens (1) was your supervisor at the Katholieke Universiteit Leuven (2009–2013). What memories do you have of your interactions with him, and to what extent did he influence your early career as a researcher?

Arnaud Dufays: My relationship with Luc Bauwens began even before my PhD, whilst I was working on my final-year dissertation. He set me a daunting challenge: to replicate a complex paper on Bayesian statistics. I remember getting stuck for two weeks on a particularly difficult algorithm, to the point where I was thinking about it constantly, even during my holidays. Then, it all clicked. That moment of clarity, followed by the successful completion of my dissertation, was a turning point: not only did it earn me an offer of a PhD from him, but above all it cemented my interest in the Bayesian approach, which is very different from classical statistics.

As my PhD supervisor, Luc Bauwens gave me a great deal of intellectual freedom whilst maintaining high standards regarding the structure of my work. I still remember my first drafts coming back covered in red! He taught me that scientific rigour also depends on clarity of writing in English. He was a constant source of support, tirelessly proofreading my ‘job market paper’ (2) even though he was not a co-author. Through seminars and our discussions, I acquired a dual statistical background, Bayesian and frequentist (3). This is a valuable asset today: juggling these two perspectives forces me to be precise in my interpretations.

You then continued to work with him, publishing papers in leading journals. What were you interested in?

Arnaud Dufays: We have tackled a fundamental problem in economics: the world is changing, but traditional models often assume that it remains stable (‘stationary’). Our work (4) has focused on modelling time-series data, both in macroeconomics (to forecast inflation or GDP) and in finance (to estimate market volatility).

Drawing on Bayesian statistics, the key innovation in our approach has been to introduce flexibility. In practical terms, we have developed models capable of recognising their own limitations: they learn to identify ‘structural breaks’—those points of discontinuity where past trends are no longer sufficient to explain future developments. This is crucial for financial volatility, which is unobservable and unstable.

These approaches emerged around the time of my PhD thesis (5) because they are computationally intensive. The exponential growth in computing power between 1995 and 2015 enabled us to move beyond simplistic theoretical models (based on assumptions valid only for very large samples) to build complex algorithms capable of adapting to the data, where classical statistics often remained more rigid.

You are an expert in the Bayesian method. What exactly is it? Why do you think it is widely underestimated, or even disparaged?

Arnaud Dufays: The Bayesian approach is based on a single fundamental equation: Bayes’ theorem. It allows us to update our beliefs (our uncertainty) as new data becomes available. Unlike the classical approach, which treats parameters as fixed constants, we treat them as random variables.

It is mainly criticised for two reasons. Firstly, it requires the definition of an “a priori” (our initial beliefs), which is often perceived as subjective. Secondly, it entails a significant computational cost, as it requires users to code their own simulation algorithms rather than using “off-the-shelf” formulas.

However, these criticisms deserve to be qualified...

Arnaud Dufays: On the one hand, modern data science methods (such as LASSO or RIDGE) are in fact closely linked to the Bayesian approach, as they impose constraints equivalent to our prior beliefs. On the other hand, the Bayesian approach is a major asset in specific situations. For example, in environments with very little information (“Zero Shot Prediction”). For example, when the euro was introduced, we had no historical data; the Bayesian approach then made it possible to construct forecasts based on prior distributions derived from other currencies. In portfolio management too: this approach offers the ability to formally incorporate the investor’s views on the future of the market in order to optimise asset allocation, much like the famous Black-Litterman approach (6). Or, in the case of one-off events, whereas classical statistics rely on repetition, Bayesian methods can assign a probability to a single event. Stephen Unwin, in an interesting book, even illustrated this logic by attempting to calculate the probability of God’s existence (7). Beyond the book’s conclusion, it is the intellectual approach that is relevant: treating each philosophical argument as a “data point” that updates an initial probability.

Your courses at EDHEC focus mainly on classical (i.e. frequentist) statistics. Does your expertise as a Bayesian researcher nevertheless influence the way you teach these concepts to students?

Arnaud Dufays: Absolutely. Paradoxically, it is my background in Bayesian statistics that helps me make classical statistics more accessible. Bayesian research is fundamentally linked to simulation: we use computers to manipulate probability distributions in order to understand complex phenomena.

I apply this philosophy in my lessons. Many statistical concepts (such as the normal distribution, the law of large numbers or confidence intervals) can seem dry and abstract to students. Rather than limiting myself to theoretical definitions, I use simulation to provide a dynamic exploration of these concepts. By seeing distributions take shape before their eyes, students develop a natural intuition for chance and uncertainty. My aim is for them to move beyond the mechanical application of formulas to truly understand the mechanics of the data they will be handling in their future careers.

References

(1) A Doctor of Economics from UCLouvain and winner of the Leonard J. Savage Prize (1984), Luc Bauwens has been a professor of economics since 1991. A leading figure at CORE, which he chaired from 2010 to 2013, he is a world-renowned researcher. His seminal work in Bayesian statistics and time series analysis has been published in the discipline’s most prestigious journals, such as the Journal of Econometrics and the Journal of Applied Econometrics. - Find out more (CV in PDF) - https://perso.uclouvain.be/luc.bauwens/LBAUWENS.pdf

(2) Arnaud Dufays, Infinite-State Markov-Switching for Dynamic Volatility, Journal of Financial Econometrics, Volume 14, Issue 2, Spring 2016, Pages 418–460, https://doi.org/10.1093/jjfinec/nbv017

(3) Bayarri, M. J., & Berger, J. O. (2004). The interplay of Bayesian and frequentist analysis - https://projecteuclid.org/journals/statistical-science/volume-19/issue-1/The-Interplay-of-Bayesian-and-Frequentist-Analysis/10.1214/088342304000000116.pdf

(4) 
a. Bauwens, L., Dufays, A., & Rombouts, J. V. (2014). Marginal likelihood for Markov-switching and change-point GARCH models. Journal of Econometrics, 178, 508-522 - https://www.sciencedirect.com/science/article/abs/pii/S030440761300167X

b. Bauwens, L., De Backer, B., & Dufays, A. (2014). A Bayesian method of change-point estimation with recurrent regimes: Application to GARCH models. Journal of Empirical Finance, 29, 207-229 - https://www.sciencedirect.com/science/article/abs/pii/S0927539814000681

c. Bauwens, L., Carpantier, J. F., & Dufays, A. (2017). Autoregressive moving average infinite hidden Markov-switching models. Journal of Business & Economic Statistics, 35(2), 162-182 - https://www.tandfonline.com/doi/abs/10.1080/07350015.2015.1123636

d. Augustyniak, M., Bauwens, L., & Dufays, A. (2019). A new approach to volatility modeling: The factorial hidden Markov volatility model. Journal of Business & Economic Statistics, 37(4), 696-709 - https://corpus.ulaval.ca/server/api/core/bitstreams/a821c6dd-e9d1-4d4f-84b7-45889cf5e1a5/content

(5) Dufays, A. (2013), Modeling structural changes in volatility

(6) Black, F., & Litterman, R. (1990). Asset allocation: combining investor views with market equilibrium. Goldman Sachs Fixed Income Research, 115(1), 7-18 - https://scispace.com/pdf/asset-allocation-combining-investor-views-with-market-20dnxng7h5.pdf

(7) Unwin, S. D. (2004). The probability of god: a simple calculation that proves the ultimate truth. Forum Books - https://www.christianbook.com/probability-simple-calculation-proves-ultimate-ebook/stephen-unwin/9781400097548/pd/19033EB