We will discuss the solution of eigenvalue problems associated with partial differential equations (PDE)s that can be written in the generalised form Ax = λMx, where the matrices A and/or M may depend on a scalar parameter. Parameter dependent matrices occur frequently when stabilised formulations are used for the numerical approximation of PDEs. With the help of classical numerical examples we will show that the presence of one (or both) parameters can produce unexpected results.

Hessian-dependent functionals play a pivotal role in a wide latitude of problems in mathematics. Arising in the context of differential geometry and probability theory, this class of problems find applications in the mechanics of deformable media (mostly in elasticity theory) and the modelling of slow viscous fluids. We study such functionals from three distinct perspectives.

We present a theoretical analysis of the Weak Adversarial Networks (WAN) method, recently proposed in [1, 2], as a method for approximating the solution of partial differential equations in high dimensions and tested in the framework of inverse problems. In a very general abstract framework.

Analogies between financial markets and critical phenomena have long been observed empirically. So far, no convincing theory has emerged that can explain these empirical observations. Here, we take a step towards such a theory by modeling financial markets as a lattice gas.

Wave propagation and scattering problems are of huge importance in many applications in science and engineering - e.g., in seismic and medical imaging and more generally in acoustics and electromagnetics.

In this short course, we will introduce some elements in deriving the hp a posteriori error estimate for a high-order unfitted finite element method for elliptic interface problems. The key ingredient is an hp domain inverse estimate, which allows us to prove a sharp lower bound of the hp a posteriori error estimator.

The statistical modeling of spatial and extreme events provides a framework for the development of techniques and models to describe natural phenomena in a variety of environmental, geoscience, and climate science applications. In a changing climate, various natural hazards, such as wildfires, are believed to have evolved in frequency, size, and spatial extent, although regional responses may vary.

This Ph.D. research focuses on proposing new statistical methods for two types of time series data: integer-valued data and multivariate nonstationary extreme data. For the former, the researcher proposes a novel approach to building an integer-valued autoregressive (INAR) model that offers the flexibility to specify both marginal and innovation distributions, leading to several new INAR processes. For the latter, the researcher proposes new extreme value theory methods for analyzing multivariate nonstationary extreme data, specifically EEG recordings from patients with epilepsy. Two extreme-value methods, Conex-Connect and Club Exco, are proposed to study alterations in the brain network during extreme events such as epileptic seizures.

Risk assessment for natural hazards and financial extreme events requires the statistical analysis of extreme events, often beyond observed levels. The characterization and extrapolation of the probability of rare events rely on assumptions about the extremal dependence type and about the specific structure of statistical models. In this thesis, we develop models with flexible tail dependence structures, in order to provide a reliable estimation of tail characteristics and risk measures. Our novel methodologies are illustrated by a range of applications to financial, climatic, and health data.

Refined characterizations of the probabilistic behavior of a stationary time-series by focusing on re normalized Markov processes that are conditioned to attain an extreme event, subject to the level of the extremity tending to the upper end point of the marginal distribution

Theoretical and practical aspects associated with the limiting distributions of block-maxima and peaks-over-threshold events in the case of stationary time-series data. Special emphasis will be placed on the extremal index, a key measure of extremal dependence that allows us to quantify the degree of clustering at the tail of a time-series.

This dissertation consists of four major contributions to subasymptotic modeling of multivariate and spatial extremes. The dissertation proposes a multivariate skew-elliptical link model for correlated highly-imbalanced (extreme) binary responses, and shows that the regression coefficients have a closed-form unified skew-elliptical posterior with an elliptical prior.

Randomized experiments are the gold standard for causal inference. In experiments, usually, one variable is manipulated and its effect is measured on an outcome. However, practitioners may also be interested in the effect of simultaneous interventions on multiple covariates on a fixed target variable.

In this thesis, we develop new flexible sub-asymptotic extreme value models for modeling spatial and spatio-temporal extremes that are combined with carefully designed gradient-based Markov chain Monte Carlo (MCMC) sampling schemes and that can be exploited to address important scientific questions related to risk assessment in a wide range of environmental applications. The methodological developments are centered around two distinct themes, namely (i) sub-asymptotic Bayesian models for extremes; and (ii) flexible marked point process models with sub-asymptotic marks. In the first part, we develop several types of new flexible models for light-tailed and heavy-tailed data, which extend a hierarchical representation of the classical generalized Pareto (GP) limit for threshold exceedances. Spatial dependence is modeled through latent processes. We study the theoretical properties of our new methodology and demonstrate it by simulation and applications to precipitation extremes in both Germany and Spain.

The statistical modeling of extreme natural hazards is becoming increasingly important due to climate change, whose effects have been increasingly visible throughout the last decades. It is thus crucial to understand the dependence structure of rare, high-impact events over space and time for realistic risk assessment. For spatial extremes, max-stable processes have played a central role in modeling block maxima. However, the spatial tail dependence strength is persistent across quantile levels in those models, which is often not realistic in practice. This lack of flexibility implies that max-stable processes cannot capture weakening dependence at increasingly extreme levels, resulting in a drastic overestimation of joint tail risk. 

Rare, low-probability events often lead to the biggest impacts. The goal of the Extreme Statistics (extSTAT) research group at KAUST is to develop cutting-edge statistical approaches for modeling, predicting and quantifying risks associated with these extreme events in complex systems arising in various scientific fields, such as climate science and finance.  In particular, the work that we develop and continue to refine has a direct potential impact to climate scientists and related stakeholders, such as engineers and insurers, who have realized that under climate change, the greatest environmental, ecological, and infrastructural risks and damages, are often caused by changes in the intensity, frequency, spatial extent, and persistence of extreme events, rather than changes in their average behavior. However, while datasets are often massive in modern day applications, extreme events are always scarce by nature. This makes it very challenging to provide reliable risk assessment and prediction, especially when extrapolation to yet-unseen levels is required.  To overcome these existing limitations, the extSTAT research group develops novel methods that transcend classical extreme-value theory to build new resilient statistical models, as well as computationally efficient inference methods, which improve the prediction of rare events in complex, high-dimensional, spatio-temporal, non-stationary settings. In this talk, I will provide an overview of my group's recent research activities and future directions with a focus on core statistical methodology contributions. The technical part of the talk will describe selected research highlights, which include (but are not limited to) the development of new flexible sub-asymptotic models applied to assessing contagion risk among leading cryptocurrencies, the development of a novel low-rank spatial modeling framework applied to estimating extreme hotspots in high-resolution Red Sea surface temperature data, and the development specialized spatio-temporal point process models applied to predicting devastating rainfall-induced landslides in a region of Italy. I will conclude my talk with an outlook on my future research plans. Motivated by methodological obstacles that arise with “big models” for complex extremes data, as well as new substantive challenges in collaborative work at KAUST, we will embark on the development of fundamentally superior models that have an intrinsically sparse probabilistic structure, as well as new "hybrid" methods that combine the strength of (parametric) models from extreme-value theory with the pragmatism and predictive power of (nonparametric) machine learning algorithms, thus opening the door to interpretable and “extreme-ly” accurate predictive models for rare events in unprecedented dimensions.

Droughts, high temperatures and strong winds are key causes of the recent bushfires that have touched a major part of the Australian territory. Such extreme events seem to appear with increasing frequency, creating an urgent need to better understand the behavior of extreme environmental phenomena.

2019 Statistics and Data Science Workshop confirmed speakers include Prof. Alexander Aue, University of California Davis, USA, Prof. Francois Bachoc, University Toulouse 3, France, Prof. Rosa M. Crujeiras Casais, University of Santiago de Compostela, Spain, Prof. Emanuele Giorgi, Lancaster University, UK, Prof. Jeremy Heng, ESSEC Asia-Pacific, Singapore, Prof. Birgir Hrafnkelsson, University of Iceland, Iceland, Prof. Ajay Jasra, KAUST, Saudi Arabia, Prof. Emtiyaz Khan, RIKEN Center for Advanced Intelligence Project, Japan, Prof. Robert Krafty, University of Pittsburgh, USA, Prof. Guido Kuersteiner, University of Maryland, USA, Prof. Paula Moraga, University of Bath, UK, Prof. Tadeusz Patzek, KAUST, Saudi Arabia, Prof. Brian Reich, North Carolina State University, USA, Prof. Dag Tjostheim, University Bergen, Norway, Prof. Xiangliang Zhang, KAUST, Saudi Arabia, Sylvia Rose Esterby, University of British Colombia, Canada, Prof. Abdel El-Shaarawi, Retired Professor at the National Water Research Institute, Canada. View Workshop schedule and abstracts here.

Extreme environmental events such as droughts, floods and heat-waves take place in space and time, and it is necessary to take this into account when evaluating their risks and estimating their probabilities.  During this seminar, I will review some classical and more recent work on this topic, focusing on the modeling of univariate and spatial extremes. The ideas will be illustrated by applications to peak river flow data from the UK, and heavy rainfall close to Jeddah.

Different scientific branches have the potential to develop topics which would provide visibility and fame. However, comparable if not greater milestones can be achieved when researchers from totally different fields join their efforts. This seminar will summarize the scientific journey of a former member of KAUST, which spent three years here as a postdoc in statistics coming from a pure geological background, combining the best out of the two worlds. Examples of the latest researches will be provided in the context of space, time and space-time statistics, bridging it with the underlying geoscientific research questions.

I will highlight the main contributions in the field of coded cooperative communications, where at first a study on the performance analysis of network-coded distributed coding schemes with different strategies for handling the relay-error propagation problem will be presented. Furthermore, a study proposing a relay selection scheme based on network-coded soft information relaying will be presented. The introducing of the Rayleigh-Gaussian model, which is applied to the forwarded relay soft symbols, have shown ability to give better performance in dealing with error propagation, and allowed us to give a tractable performance analysis of network-coded schemes under Rayleigh fading channels.

Extreme value theory (EVT) deals with the asymptotic distributions of the extremes (maximum or minimum) of a set of N random variables, as N grows large. EVT is a powerful tool to analyze the performance of generalized user selection in modern wireless Communication systems. In this talk, we will provide an overview of EVT and its application to the performance of generalized user selection for multiuser traditional wireless and cognitive radio networks.