Univariate and Multivariate Regression on Extreme Values
Funded by Villum Foundation, 2014-2018
An important theme in statistics is the study of relationships between two or more variables.
Firstly, in regression analysis, the main objective is to describe how a variable of primary interest, the dependent or response variable, depends on one or more explanatory variables. Although one is classically interested in the estimation of the mean of the dependent variable, there are many practical instances where it is more relevant to study the extreme rather than the average responses.
For instance, insurance companies safeguard themselves against major losses by entering re-insurance contracts. For the reinsurers it is thus of crucial importance to have a precise estimate of the tail of the claim size distribution. Linking this tail to so-called risk factors, like insured capital and environmental factors, will allow to make a more adequate assessment of the risks involved and consequently to a better determination of the premium levels.
Secondly, in multivariate statistics one aims at inferring about the joint stochastic behaviour of several variables. Also here, of particular interest is the situation where all variables are simultaneously extreme, and as such focus will be on the estimation of the extreme dependence, since the combined effect of several extreme variables might be much more severe than when only one (or few) of them is extreme.
For instance, extreme temperatures and high levels of pollutants like ground-level ozone and particulate matter pose a major threat to human health, so it is crucial to have an accurate estimate of their dependencies at extreme levels. This issue becomes increasingly important in view of global warming.
In the project group we developed novel techniques that can be used to infer about extreme events in presence of random explanatory variables. The project is of a theoretical, probabilistic nature and will fill a gap in the methodology that is available for inferring on extreme events. It will also form the basis for subsequent statistical applications in various scientific disciplines.
For more information see: https://imada.sdu.dk/~yuri/villum.htm.
In current research we focus on extensions of the results obtained from the Villum project. In particular, we study the estimation of multivariate risk measures using multivariate extreme value theory and results from empirical process theory. This is pursued in collaboration with Jing Qin (SDU), Armelle Guillou (University of Strasbourg), Mikael Escobar-Bach (University of Angers), Jacob Hjelmborg (SDU) and a Ph.D. student.
The pace and shape of mortality in primates
Funded by the The Max Planck Institute for Demographic Research (MPIDR)
Age specific mortality within a population can be summarized in terms of the pace of life, based on measures such as life expectancy or generation time, and in terms of the shape of mortality, which provides a measure of the variability in ages at death. These two measures are amongst the most fundamental building blocks in the demographer’s tool kit, and are used in a wide range of disciplines as tools to explain mortality and its relationship with, for instance, income inequality, sociality, etc.
In Colchero et al. (2016) we analyzed how life expectancy (pace) and lifespan equality (shape) changed within human populations and among related species such as humans, chimpanzees, gorillas, etc. We found a surprising linear trend in the relationship between life expectancy and lifespan equality in humans, and a less steep relationship between species. The extremely regular nature of this relationship raised two main questions: (i) what is the explanation for the regular relationship? and (ii) is this regular relationship also seen within other primate species?
In order to answer these questions, we organized the Odense Pace-shape of Primate Mortality Workshop at the University of Southern Denmark in December 2017, funded by the Max Planck Institute for Demographic Research, where experts from around the world gathered to discuss and analyze 18 long-term datasets from different populations of chimpanzees, gorillas, baboons, capuchin monkeys, etc.
Our preliminary analyses show a strong linear relationship between pace and shape within several different species of primates that seems to recapitulate the within-human relationship, but each species has a different intercept and possibly a different slope. Our aim is to explain what is driving the extreme regularity within species and to understand the variation between species.
Metabolomics of Patients with Glucocorticoid-induced Diabetes Mellitus
This interdisciplinary project is a collaboration between researchers from Nordsjællands Hospital (Dept. of Endocrinology and Nephrology), SDU (Dept. of Biochemistry and Molecular Biology, Dept. of Mathematics and Computer Science, Dept. of Public Health), the Danish Centre for Research in Type 2 Diabetes and the Medical University Graz (Dept. of Dermatology and Venerology).
We study and analyze the metabolome of patients with glucocorticoid-induced diabetes mellitus (GIDM) to improve the understanding of the disease. Methods from statistical learning are applied to metabolomics data to investigate whether it is possible to distinguish patients with type 2 diabetes from those with GIDM better than currently possible. Variable selection with error control is used to identify relevant metabolites.