The Extreme Statistics (XSTAT) research group that Raphaël Huser leads at KAUST focuses on the following main lines of research:

1. Statistics of extremes and risk assessment: We develop specialized statistical models for low-probability-high-impact extreme events, that have appealing statistical properties for tail extrapolation and the assessment of future (potentially more extreme) risk. These include:
   • the development of multivariate, spatial or spatio-temporal models that are flexible in their joint tail behavior, in order to capture different asymptotic dependence regimes in a parsimonious way;
   • the development of models that accommodate nonstationarity in space and/or time, in their marginal distributions and/or their dependence structure;
   • the development of deep quantile regression models for extremes, which combine justified extreme-value regression models with deep-learning methods, in order to efficiently extract complex relationships between an extreme response and covariates.

      

2. Efficient inference methods for complex models and big data: Beyond creating new models with interesting statistical properties, one important aspect is to be able to efficiently fit these complex models to massive datasets. Often, classical inference approaches based on the full likelihood are not available or are computationally intractable, so alternative approaches that are both fast and accurate need to be designed. These include:
   • likelihood-based approaches that rely on lower-dimensional, sparse, or low-rank methods, as well as other numerical approximations (e.g., composite likelihoods, the Vecchia approximation, local likelihoods, graphical methods and SPDE-based models, INLA, carefully-designed Bayesian hierarchical models, etc.); 
   • likelihood-free approaches, such as neural Bayes estimators (see below).

      

3.  Neural Bayes estimators: One important area of current research in the XSTAT group is the development of general-purpose, likelihood-free, fast and statistically-efficient neural Bayes estimators. Essentially, these estimators are neural networks that approximate Bayes estimators, which makes them attractive both from a statistical and a computational perspective. These estimators are also amortized in the sense that, although the computational time and effort needed to initially train the underlying neural network can be substantial, once trained, inference from observed data that conform with the chosen neural-network architecture is extremely fast. Being both deeply anchored into statistical decision theory and relying on advanced deep-learning techniques, neural Bayes estimators are currently emerging as a paradigm shift challenging traditional statistical inference techniques for complex models with intractable likelihoods. The XSTAT research group (with collaborators) is contributing extensively to the early developments of such estimators and their application primarily to spatial (e.g., extreme) and multivariate models.

    

4. Applications: Our methodological contributions are often motivated and fed by a wide variety of real data applications in climate and earth sciences, finance and neuroscience. These include: 
   • the modeling of natural hazards (e.g., heavy rainfall, peak river flows, heat waves, extreme sea surface temperatures, strong wind gusts, extreme wave heights, high pollution levels, devastating landslides, dangerous wildfires) and the assessment of climate change's impacts on such extreme events; 
   • the assessment of financial risk (e.g., turbulence in stock markets or cryptomarkets); 
   • the characterization of brain signals during extreme stimuli (e.g., epileptic seizures).