Dear Colleagues, The *Department of Mathematics* of the *University of Luxembourg* (*DMATH*) is seeking an excellent candidate for a *PhD position* in the area of *Mathematical Statistics*, with an expected starting date in *2026*. *-----------------------* *Supervisor:* Prof. *Yannick Baraud* (https://math.uni.lu/baraud/Home.html) *PhD topic:* *Classical Bayesian methods can be used to construct estimators with good statistical properties. For example, when the data are i.i.d. and come from a distribution belonging to a parameterised model with a suitable prior distribution, numerous studies show that the posterior distribution is concentrated around the parameter associated with the distribution of the data.* *Despite their popularity, these methods nevertheless have certain limitations. In particular, when the data-generating distribution does not belong to the family of distributions chosen as the model, the estimators obtained may be of poor quality, even when the model provides a good approximation of the truth. This situation can arise, for example, when the sample contains a few outliers due to measurement or transcription errors. More generally, it occurs when the statistical model is only a simplification of reality, which is often the case in practice. The statistical method is then said to suffer from a lack of robustness as it produces unstable estimators that are sensitive to small deviations from the assumed model.* *In this PhD proposal, we offer the opportunity to study a robust alternative to classical Bayesian methods. This is a recent approach, the main properties of which were established in [1] in the context of density estimation. The aim of this PhD proposal is to understand the mathematics behind these new techniques and to extend it beyond density estimation. * *A candidate for this position must have a strong background in analysis, probability and mathematical statistics as well as a taste for theory. * [1] Y. Baraud. From robust tests to Bayes-like posterior distributions. Probab. Theory Related Fields, 188(1-2):159–234, 2024. --------------------------- The successful candidate will join a dynamic research environment with strong international collaborations and access to high-level scientific infrastructure. For further details concerning the position, application procedure, and eligibility requirements, please contact directly Prof. Baraud at the address yannick.baraud@uni.lu Please feel free to circulate this announcement within your networks. Best regards, Giovanni Peccati -- Prof. Giovanni Peccati ------------------------------------------ Head of the Department of Mathematics Faculty of Science, Technology and Medicine ------------------------------------------ University of Luxembourg ------------------------------------------ President of the Luxembourg Mathematical Society https://math.uni.lu/sml/ ------------------------------------------ homepage: http://sites.google.com/site/giovannipeccati/home E-mail: giovanni.peccati@gmail.com