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.
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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.
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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
Please feel free to circulate this announcement within your networks.
Best regards,
Giovanni Peccati