PhD Position F/M INFERENCE FOR EXTREME DATA IN A UNIVARIATE DEPENDENT SETTING

The Inria center at Université Côte d'Azur includes 42 research teams and 9 support services. The center’s staff (about 500 people) is made up of scientists of different nationalities, engineers, technicians and administrative staff. The teams are mainly located on the university campuses of Sophia Antipolis and Nice as well as Montpellier, in close collaboration with research and higher education laboratories and establishments (Université Côte d'Azur, CNRS, INRAE, INSERM ...), but also with the regional economic players.

With a presence in the fields of computational neuroscience and biology, data science and modeling, software engineering and certification, as well as collaborative robotics, the Inria Centre at Université Côte d'Azur  is a major player in terms of scientific excellence through its results and collaborations at both European and international levels.

This PhD position is part of the “Thèses Tandem” program, a joint initiative
between the Université de Montpellier (France) and the Université de Sherbrooke
(Canada).

Two complementary PhD projects are offered through this collaboration, each
focusing on a different yet interconnected aspect of univariate extreme value modeling
under dependence. The selected candidates will benefit from shared supervision,
close collaboration between the two universities, and regular research
exchanges. The program includes funding for a work computer, travel to national and
international conferences, and several research stays at Université de Sherbrooke,
in Québec, Canada.

The aim of this thesis project is to develop frequentist and Bayesian inference techniques for estimating the limit distribution of themaximum under dependency assumptions. Bayesian methods are particularly suited to situations where information is scarce oruncertain - which is typically the case in the analysis of extremes

Univariate extreme value theory (EVT) states that the maximum of a sequence
of independent, identically distributed random variables converges to a Generalized
Extreme Value (GEV) distribution. However, the assumption of independence is
often unrealistic in real-world applications, where data are typically temporally or
spatially correlated - e.g., wave heights, temperature records, pollution levels, or
financial returns.
Pioneering work by Leadbetter (1974, 1983) relaxed the independence assumption
by introducing asymptotic dependence conditions, allowing a form of “quasiindependence”
between extreme events. More recently, copula-based approaches  have enabled the separate modeling of marginal behavior and dependence structure (Sklar, 1959), significantly advancing the field, especially in multivariate settings.
We refer to Nelsen (2006), Joe (2015), or Durante and Sempi (2015) for textbook introductions.
A different point-of-view was proposed by Herrmann, Hofert, and Nešlehová (2024), who established convergence conditions for the maximum in a dependent univariate setting using copulas. This generalizes the Fisher-Tippett-Gnedenko theorem to sequences of dependent variables.

Supervision team : Gwladys Toulemonde (IMAG, Université de Montpellier and
Inria LEMON) and Nicolas Meyer (IMAG, Université de Montpellier and Inria LEMON)
with Klaus Herrmann and Eric Marchand (Equipe de statistique, Université
de Sherbrooke)

The aim of this thesis project is to develop frequentist and Bayesian inference
techniques for estimating the limit distribution of the maximum under dependency
assumptions. Bayesian methods are particularly suited to situations where
information is scarce or uncertain - which is typically the case in the analysis of
extremes, see Beirlant et al. (2004, Chapter 11) or Bousquet & Bernardara (2021,
Chapter 11). By introducing flexible prior distributions on the parameters, we can
obtain :
— credibility intervals (rather than simple confidence intervals),
— density prediction for extreme observations,
— better consideration of dependency structure, particularly in exchangeable
models, such as those discussed in Herrmann, Hofert & Nešlehová (2024).

The thesis will thus aim to develop and study estimators and evaluate their performance
on simulated and real data, for example meteorological or financial data.

M2 or engineering degree in statistics.
Strong background in mathematics, particularly statistics and probability theory, proficiency in R and/or Python programming

• Subsidized meals
• Partial reimbursement of public transport costs
• Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
• Possibility of teleworking (after 6 months of employment) and flexible organization of working hours
• Professional equipment available (videoconferencing, loan of computer equipment, etc.)
• Social, cultural and sports events and activities
• Access to vocational training
• Contribution to mutual insurance (subject to conditions)

Duration: 36 months
Location: Sophia Antipolis, France
Gross Salary per month: 2200€ (2025).