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 Mat\'ern family of covariance functions is currently the most commonly used for the analysis of geostatistical data due to its ability to describe different smoothness behaviors. Yet, in many applications the smoothness parameter is set at an arbitrary value.

Statistical analysis for the purpose of prediction is preferably accompanied by uncertainty quantification, often in the form of prediction intervals. Deep learning approaches have been extensively shown to provide accurate point predictions in many applications.

The modeling of spatio-temporal and multivariate spatial random fields has been an important and growing area of research due to the increasing availability of space-time-referenced data in a large number of scientific applications. In geostatistics, the covariance function plays a crucial role in describing the spatio-temporal dependence in the data and is key to statistical modeling, inference, stochastic simulation, and prediction. Therefore, the development of flexible covariance models, which can accommodate the inherent variability of the real data, is necessary for advantageous modeling of random fields. This thesis is composed of four significant contributions in the development and applications of new covariance models for stationary multivariate spatial processes, and nonstationary spatial and spatio-temporal processes. Firstly, this thesis proposes a semiparametric approach for multivariate covariance function estimation with flexible specification of the cross-covariance functions via their spectral representations. The flexibility in the proposed cross-covariance function arises due to B-spline based specification of the underlying coherence functions, which in turn allows for capturing non-trivial cross-spectral features. The proposed method is applied to model and predict the bivariate data of particulate matter concentration and wind speed in the United States. Secondly, this thesis introduces a parametric class of multivariate covariance functions with asymmetric cross-covariance functions. The proposed covariance model is applied to analyze the asymmetry and perform prediction in a trivariate data of particulate matter concentration, wind speed and relative humidity in the United States.
 Thirdly, the thesis presents a space deformation method which imparts nonstationarity to any stationary covariance function. The proposed method utilizes the functional data registration algorithm and classical multidimensional scaling to estimate the spatial deformation. The application of the proposed method is demonstrated on precipitation data from Colorado, United States. Finally, this thesis proposes a parametric class of time-varying spatio-temporal covariance functions, which are stationary in space but nonstationary in time. The proposed time-varying spatio-temporal covariance model is applied to study the seasonality effect and perform space-time predictions in the daily particulate matter concentration data from Oregon, United States.

This thesis presents a set of quantile analysis methods for multivariate data and multivariate functional data, with an emphasis on environmental applications, and consists of four significant contributions.

Environmental statistics plays an important role in many related applications, such as weather-related risk assessment for urban design and crop growth. However, modeling the spatio-temporal dynamics of environmental data is challenging due to their inherent high variability and nonstationarity. This dissertation focuses on the modeling, simulation, and prediction of spatio-temporal processes using statistical techniques and machine learning algorithms, especially for nonstationary processes.

Abstract

The analysis of solar irradiance ha

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.

In this talk, we explore a graphical model representation for the stochastic coefficients relying on the specification of the sparse precision matrix. Sparsity is encouraged in an L1-penalized likelihood framework. Estimation exploits a majorization-minimization approach. The result is a flexible nonstationary spatial model that is adaptable to very large datasets.