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 Integrated Nested Laplace Approximations (INLA) method has become a commonly used tool for researchers and practitioners to perform approximate Bayesian inference for various fields of applications. It has become essential to incorporate more complex models and expand the method’s capabilities with more features. In this dissertation, we contribute to the INLA method in different aspects.

The commonly used leave-one-out and K-fold cross-validation methods are not suitable for structured models with multiple prediction tasks. To overcome this limitation, we introduce leave-group-out cross-validation, which allows groups to adapt to different tasks. We propose an automatic group construction method and provide an efficient approximation for latent Gaussian models. Moreover, this method is conveniently implemented in the R-INLA software.

Latent Gaussian models (LGM) are widely used but struggle with certain datasets that contain non-Gaussian features, such as sudden jumps or spikes. This dissertation aims to provide tools for researchers to check the adequacy of the fitted LGM (criticism); if the check fails, offer efficient and user-friendly implementations of latent non-Gaussian models, which lead to more robust inferences (robustification).

Bayesian inference is particularly challenging on hierarchical statistical models as computational complexity becomes a significant issue. Sampling-based methods like the popular Markov Chain Monte Carlo (MCMC) can provide accurate solutions, but they likely suffer a high computational burden.

A competing event is any event that makes it impossible for the outcome of interest to occur. The presence of competing events requires us to be careful about the interpretation of classical causal estimands. In particular, the average treatment effect captures effects through the competing event, pathways that may not be of primary interest. As a solution, we suggest the separable effect, inspired by Robins and Richardson’s extended graphical approach. We will give criteria that allow different interpretations of the separable effects and present identification conditions that can be evaluated in causal graphs.

The statistical analysis based on the quantile method is more comprehensive, flexible, and not sensitive against outliers compared to the mean methods. The study of the joint disease mapping focuses on the mean regression. This means they study the correlation or the dependence between the means of the diseases by using standard regression. However, sometimes one disease limits the occurrence of another disease. In this case, the dependence between the two diseases will not be in the means but in the different quantiles; thus, the analyzes will consider a joint disease mapping of high quantile for one disease with low quantile of the other disease.

Abstract

In this talk I will discuss statistical models which incorporate temperature response to the radiative forcing components. The models can be used to estimate important climate sensitivity measures and give temperature forecasts. Bayesian inference is obtained using the methodology of integrated nested Laplace approximation and Monte Carlo simulations. The resulting approach will be demonstrated in analyzing instrumental data and Earth system model ensembles.

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.

Joint models have received increasing attention during recent years with extensions into various directions; numerous hazard functions, different association structures, linear and non-linear longitudinal trajectories amongst others. They gained popularity amongst practitioners by the ability to incorporate various data sources. In this talk, we will introduce joint models and provide some conceptual ideas about their use and necessity. Also, we will illustrate how these models can be formulated as Latent Gaussian Models and hence be implemented using R-INLA.