The Sustainable Energies Chair of the Ecole Polytechnique is offering a 1-year
post-doc position, renewable once and starting as soon as possible, and in any
case before june 1st, 2025, on a subject related to improving the objectivity of
Bayesian modeling rules in view of supporting interpretable decision. The sit-
uations concerned with this quantification problem of uncertain knowledge are
numerous, and are particularly motivated within the framework of this work by
applications interesting the field of decarbonated energies.
The technical motivation for this work stems from the research program pro-
posed in [4], that extends the proposals made in [3]. Bayesian modeling choices
play an important role in the context of forecasting and decision support through
statistical learning applied to costly or rare data. These are characteristic of
the risk situations affecting the industrial world. Their promise is to be able to
model the uncertain knowledge required to inform models in addition to avail-
able data, or even in their absence in the event of a regime change. Major
applications related to decarbonated energies are the following (among others):
• rapid location of nuclear material in waste packages, in order to apply
focused spectrometry techniques to identify fission products;
• the reliability of important or even critical industrial components, such as
steam generators, batteries, valves, etc. ;
• quantification of the intensity of extreme natural phenomena (torrential
rain, marine submersion, floods, etc.);
• calibration of technico-economic models used to optimize the design and
operation of energy parks, particularly when the depth of history is shal-
low (e.g. offshore park deployments).
1
Objectivation aims to respond to the obstacles that are generally blamed
on the corpus of existing Bayesian methods, despite their huge number [7], and
which still limit their use in proposal submitted to safety and control authorities
in the energy sector: the low repeatability of methodologies, the lack of control
over subjective elements in modeling choices, and the lack of interpretability of
models. See [12] for more details. An additional difficulty is to propose calibra-
tion rules based on the repeatability of experiments.
2 Work program
The work will aim to bring together a set of known ”methodological constraints”,
still separated, into a single approach that will extend methodologies already
established for sub-families of models (in particular exponential families and
conjugate models). Such constraints are, for instance, related to prior-data
conflict [2, 10] or q-vague convergence [1].
This approach will thus focus on defining a ”modeling continuum” limited
by objective reference priors [8, 13] and so-called ”Posterior Priors” models re-
sulting from the application of Bayes’ theorem [11, 6, 5]. Such approaches
are interpretable because they consider that the available information can be
assimilated to that provided by data not directly known, but that it can be
manipulated by explicit approximation techniques outside conjugate families
[3]. Such approaches participate to provide rules for clarifiying the meaning of
Prior Effective Sample Sizes (PESS), the definition of which is still the subject
of debate in the community (e.g., [9]).
The resulting methodology will be submitted to leading scientific journals
(e.g. Bayesian Analysis) and re-used in many sectors beyond the energy indus-
try.
3 Supervision
The work will be supervised by Professor Josselin Garnier (École Polytechnique
/ CMAP-Centre de Mathématiques Appliquées), in collaboration with Dr. Nico-
las Bousquet, senior researcher at EDF R&D. CMAP and EDF have been work-
ing together for a very long time. CEA DES, a frequent partner of EDF and
CMAP, is also keen to participate in discussions during the post-doctoral work.
The position could start at any time between september 1st, 2024, and june 1st,
2025. The earlier, the better.
The candidate should have a PhD thesis in statistics or applied mathe-
matics, with a good knowledge of Bayesian statistics. A good knowledge of
2
mathematical tools related to the approximation of probability distributions
and non-convex optimization would be a plus.
The candidate will join CMAP’s SIMPAS (Statistique Apprentissage Simu-
lation Image) team at École Polytechnique, located in Palaiseau, France. École
Polytechnique specializes in science and engineering. CMAP conducts theoret-
ical and numerical research on mathematics in interaction with other sciences
(biology, economics, computer science, mechanics, physics, etc) or in connec-
tion with industrial or societal applications. Its specialties are numerical analy-
sis, scientific computing, control, artificial intelligence, modeling, optimization,
probability, signals, statistics, etc.
The candidate will become involved in the Uncertainty Quantification the-
matic network (formerly known as GDR MASCOT-NUM). In addition, the
candidate will benefit from an industrial environment strongly interested in
this work, and from a French and international network in Bayesian modeling
(especially, the Bayesian Group at SFdS, the APPLIBUGS Group, the ISBA
Community)