ABOUT ME
Welcome to this site, mainly dedicated to my research activities, although I'll provide material concerning my teaching activities.
I'm 57. I followed an industrial career as an engineer from 1987 till 2002. But my real vocation has always been research in mathematics. I love maths for multiple reasons I'll probably describe in a forthcoming post. For familial reasons, I couldn't do a PhD after my engineering degree. Instead, I wrote and defended a PhD in 1997, besides my working hours, because I had in mind that a day or another, I could become an academic researcher. So, I'm happy without the least regret to have joined Telecom Bretagne (IMT-Atlantique, now) in 2002.
Oxyrhynchus papyrus showing fragment of Euclid's Elements, circa AD 75-125
Source: https://www.pitt.edu/~jdnorton/
During my industrial career, I got the opportunity to face various signal processing applications (speech, radar, communications, etc). As a researcher, in addition to these applications, I dealt with physiological signals for biomedical applications. This multiplicity was by no means a wandering but a true enrichment.
My experience in different applications of statistical signal processing led me to notice and deem that prior knowledge on the signals at stake is often too poor in practice to allow for standard approaches. All my ideas actually originate from this observation, which prompted me to seek new statistical signal processing methods to cope with such situations.
William of Occam, the model for William of Baskerville, the main character in Umberto Eco's 'The name of the Rose'.
The philosophy underpinning my research is strongly influenced by Occam's razor summarized by ‘Never posit pluralities without necessity’ (‘Numquam ponenda est pluralitas sine necessitate’) or 'With all things being equal, the simplest explanation tends to be the right one'. In this respect, I strive to come up with the least possible number of hypotheses encompassing the largest number of cases for which we can state algorithms that guarantee some performance and, if any, some optimality. This stance could be further discussed in connection with the the Bayesian and Non-Bayesian schools of thought. I'll try to do it in a later post. At this stage, for better insight into the 'rule of parsimony' encapsulated in Occam's razor, I find the following two points, which can be found in Wikipedia, particularly enlightening.
Ontological parsimony : ”A rule of thumb, which obliges us to favor theories or hypotheses that make the fewest unwarranted, or ad hoc, assumptions about the data from which they are derived.” Hans-Johann Glock (2004)
'For each accepted explanation of a phenomenon, there may be an extremely large, perhaps even incomprehensible, number of possible and more complex alternatives, because one can always burden failing explanations with ad hoc hypotheses to prevent them from being falsified ; therefore, simpler theories are preferable to more complex ones because they are more testable' [Wikipedia] and falsifiable in Karl Popper’s sense.
At the top of this page, I emphasize that I love mathematics. In particular, by taste and culture, I'm deeply fascinated and interested by the foundations of mathematics and the connection between mathematics and philosophy. Hence, there is an ultimate and long-term objective in my research works. Somehow in the vein of Jaynes's 'Probability theory: the logic of science', I'm working on possible new links between statistical hypothesis testing and logic, via a perspective based on category theory and more specifically, sheaf theory. More details are given in the pages dedicated to the different themes I address in my research. But, in a nutschell, the starting point is that, after all, a decision made by a statistical test on a given hypothesis is nothing else but a probabilistic truth value on the predicate corresponding to the tested hypothesis.
