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.

Cross-validation is an algorithmic technique extensively used for estimating the prediction error, tuning the regularization parameter, and choosing between competing predictive rules.

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.

In this talk, we present theoretical asymptotic results for the nonparametric estimation of the conditional density of a scalar response variable Y given the explanatory X taking values in a finite-dimensional space when the sample of observations is considered as a sequence of dependent random variables.

The standard approach to analyzing brain electrical activity is to examine the spectral density function (SDF) and identify frequency bands, defined apriori, that have the most substantial relative contributions to the overall variance of the signal. However, a limitation of this approach is that the precise frequency and bandwidth of oscillations are not uniform across cognitive demands. Thus, these bands should not be arbitrarily set in any analysis. To overcome this limitation, we propose three Bayesian Non-parametric models for time series decomposition, which are data-driven approaches that identify (i) the number of prominent spectral peaks, (ii) the frequency peak locations, and (iii) their corresponding bandwidths (or spread of power around the peaks).

During the first part of the talk we present an approach that allows for flexible analysis of multivariate non-stationary time series via dynamic models on the partial autocorrelation domain. We discuss various aspects of these models, including the use of shrinkage priors to deal with overfitting issues, as well as hierarchical extensions.

In the first part of this lecture we present a review dynamic linear models for multivariate time series and hierarchical dynamic linear models for multiple time series. Topics related to model building as well as closed form, approximate and simulation-based methods for Bayesian filtering, smoothing and forecasting within these classes of models will be discussed.

We present a framework for non-Gaussian spatial processes that encompasses large distribution families. Spatial dependence for a set of irregularly scattered locations is described with a mixture of pairwise kernels. Focusing on the nearest neighbors of a given location, within a reference set, we obtain a valid spatial process:

We discuss conditionally Gaussian dynamic linear models for analysis and forecasting of univariate time series and present simulation-based methods for Bayesian filtering and smoothing within this class of models, including Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods.

We will start by presenting the general framework of Bayesian hierarchical dynamic models (BHDM) for space-time data. Within this framework, we will consider in some detail the special case of linear dynamics. We will review MCMC estimation for conditionally linear dynamic models. We will introduce integro-differential models and give a SPDE justification that provides insights into the connections between the dynamics of the process and the properties of the kernel defining the IDE.

In this lecture we present an overview of dynamic linear models for analysis and forecasting of univariate time series. We will discuss principles for model building and methods for Bayesian filtering, smoothing and forecasting. We will illustrate the use of these models in several case studies arising in different applied areas including environmental sciences and neuroscience.

Continuing on with Lecture 1, this short course introduces various cutting-edge methods that handle survival outcome data with ultrahigh dimensional predictors, that is, when the dimension of predictors is much higher than the sample size. We will also discuss several new methods for quantifying the uncertainty of estimates in a high dimensional survival setting, a very active area in machine learning.

Though Gaussian graphical  models have been widely used in many scientific fields, relatively limited progress has been made to link graph structures to external covariates. We propose a Gaussian graphical regression model, which regresses both the mean and the precision matrix of a Gaussian graphical model on covariates. In the context of co-expression quantitative trait locus (QTL) studies, our method can determine how genetic variants and clinical conditions modulate the subject-level network structures, and recover both the population-level and subject-level gene networks.

In the era of biomedical big data, survival outcome data with high-throughput predictors are routinely collected. These high dimensional data defy classical survival regression models, which are either infeasible to fit or likely to incur low predictability because of overfitting. This short course will introduce the basic concepts of survival analysis and various cutting-edge methods that handle survival outcome data with high dimensional predictors. I will cover statistical principles and concepts behind the methods, and will also discuss their applications to the real medical examples.

Breakthroughs such as high-throughput sequencing are generating flourishing high-dimensional data that provoke challenges in both statistical analyses and interpretations.

Abstract

For over 30 years, Bayesian image analysis has provided an imp

Intrinsic connectivity networks (ICNs) refer to brain functional networks that are consistently found under various conditions, during tasks or at rest. Some studies demonstrated that while some stimuli do not impact intrinsic connectivity, other stimuli actually activate intrinsic connectivity through suppression, excitation, moderation or modification. Most analyses of fMRI data use ad-hoc methods to estimate the latent structure of ICNs. Modeling the effects on ICNs has also not been fully investigated. We propose a Bayesian Intrinsic Connectivity Network (BICNet) model, an extended Bayesian dynamic sparse latent factor model, to identify the ICNs and quantify task-related effects on the ICNs. BICNet has the following advantages: (1) It simultaneously identifies the individual and group-level ICNs; (2) It robustly identifies ICNs by jointly modeling rfMRI and tfMRI; (3) Compared to ICA-based methods, it can quantify the difference of ICN amplitudes across different states; (4) The sparsity of ICNs automatically performs feature selection, instead of ad-hoc thresholding. We apply BICNet to the rfMRI and language tfMRI data from the HCP and identify several ICNs related to distinct language processing functions.

This talk presents a new classification method for functional data. We consider the case where different groups of functions have similar means so that it is difficult to classify them based on only the mean function. To overcome this limitation, we propose the second moment based functional classifier (SMFC). Here, we demonstrate that the new method is sensitive to divergence in the second moment structure and thus produces lower rate of misclassification compared to other competitor methods. Our method uses the Hilbert-Schmidt norm to measure the divergence of second moment structure. One important innovation of our classification procedure lies in the dimension reduction step. The method data-adaptively discovers the basis functions that best capture the discrepancy between the second moment structures of the groups, rather than uses the functional principal component of each individual group, and good performance can be achieved as unnecessary variability is removed so that the classification accuracy is improved. Consistency properties of the classification procedure and the relevant estimators are established. Simulation study and real data analysis on phoneme and rat brain activity trajectories empirically validate the superiority of the proposed method.

In this talk, I will give an overview of my research which focuses on the development of innovative statistical methods and interactive visualization applications for geospatial data analysis and health surveillance. I will illustrate some of my projects in the following areas: 1. Development of new statistical methodology; 2. Development of open-source statistical software such as the R packages; 3. Health surveillance projects. Finally, I will describe my future research on innovation in data acquisition and visualization, precision disease mapping, and digital health surveillance, and how it can inform policymaking and improve population health globally.

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.