Projects
Quantile estimation for multivariate data using the multivariate generalised hyperbolic distribution KU Leuven
Quantile regression provides a rich tool for describing data distributions and allows an easy interpretation. The estimation of quantiles can be translated to the maximum likelihood framework for an asymmetric Laplace distribution. But since real-life applications often involve multiple, interrelated outcomes, statistical modelling should take this dependence into account. A possible approach is the use of the multivariate generalisation of ...
BINGE EATING AND PURGING IN COLLEGE STUDENTS: CROSS-SECTIONAL AND LONGITUDINAL MULTIVARIATE CORRELATES KU Leuven
INTRODUCTION AND BACKGROUND Binge eating and purging behaviors (BPB) are symptomatic behaviors which can be present in eating disorders and other mental disorders, as well as in non-pathological conditions. Specifically, binge eating refers to episodes during which a person rapidly consumes an excessive quantity of food while feeling a sense of loss of control; purging behaviors are inappropriate compensatory behaviors, aiming to prevent ...
Signaling a diverse range of changes in multivariate time series: A flexible kernel-based change point detection approach KU Leuven
Many scientific fields track variables through time to monitor trends, dynamics and abrupt changes. In this dissertation, we focus on the latter and aim to detect sudden distributional changes in time series data. Most of the existing change point detection methods proposed to automatically signal these abrupt shifts are univariate, targeting mean and other univariate statistics. This is an important limitation since in many applications, ...
Transitional Models in Suicidal Thoughts and Behaviors: Multivariate Longitudinal Designs KU Leuven
The proposed PhD study is part of an international collaboration between Stellenbosch University (SUN) and the Katholieke Universiteit Leuven (KU Leuven, Belgium) (Public Health Psychiatry Universitair Psychiatrisch Centrum KULeuven). It is a funded joint PhD programme (Global joint-PhD Scholarship Programme) between SUN and KU Leuven and involves a joint PhD registration at SUN and KU Leuven. Furthermore, the proposed PhD study will comply ...
Study of multivariate asymmetric distributions using univariate two-piece distributions KU Leuven
When analyzing data, among the most important questions is which distribution does appropriately describe the probabilistic model that is behind the data. In the simplest univariate setting, one of the first questions to ask is whether the distribution is symmetric, skewed to the right, the left, heavy tailed, light tailed etc. In recent years some interesting (large) parametric families of asymmetric densities have been studied. This recent ...
Generalized Askey-Wilson and q-Onsager algebras: a quantum algebraic approach to multivariate orthogonal polynomials Ghent University
The Askey-Wilson algebra was introduced as the algebraic structure behind the Askey-Wilson orthogonal polynomials. It is closely related to the q-Onsager algebra, which originates from statistical mechanics. Both algebras appear in the context of superintegrable quantum systems. Such systems are governed by a Hamiltonian which possesses a sufficient number of symmetry operators. These symmetries are invaluable tools to solve the equations of ...
Multivariate polynomial and rational interpolation and approximation. KU Leuven
In several theoretical as well as computational mathematical problems, one wants to work with complicated multivariate functions. However, in a lot of cases performing operations with these original functions is cumbersome and requires an unacceptably high computational e↵ort. A solution to this problem is to replace the original complicated function by a function that can be handled much more easily, e.g., polynomial or rational functions. ...
Nonparametric Inference Based on Depth for Multivariate Data KU Leuven
Statistical data depth is a nonparametric tool applicable to multivariate datasets in an attempt to generalize quantiles to complex data such as random vectors, random functions, or distributions on manifolds and graphs. The main idea is, for a general multivariate space M, to assign to a point x from M and a probability distribution P on M a real number D(x;P) characterizing how "centrally located" x is with respect to P. A point maximizing ...
Copula-based multivariate association measures and tail coefficients KU Leuven
The main topic of the thesis is quantification of the strength of dependence within a d-variate random vector X. The dependence structure of X is fully determined by the corresponding copula function. We investigate various ways how to summarize the strength of dependence (given by the corresponding copula) into a single number.
In particular, we focus on two types of such coefficients. The overall dependence is described by ...