Modeling risk in complex systems

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The increasing digitalization, urbanization, and interconnectedness of human economies come with growing vulnerability to natural and man-made catastrophes. Risk management and disaster preparedness are thus of paramount importance for society and sustainable development. In continuation of my previous NSERC Discovery Grant, the long-term vision of the proposed research program is to provide tractable and flexible models for risk management. My long-term goals are to develop statistical models and inference techniques to unravel complex dependence patterns in large collections of risk factors and to quantify causal effects on, and of, extremes. The quantification of complex and possibly extreme risks requires techniques beyond traditional approaches rooted in normality, correlation, and regression. The first short term objective is to advance my ongoing work on copula models, which can capture relationships that can't be adequately accounted for by traditional distributions. Using rank-based techniques, I will develop methodology for copula models for mixed data and devise tests of independence for arbitrary distributions in high dimensions. My recent results on the empirical multilinear copula process will also be used to validate generalized linear models. I further aim to find dependence patterns in large collection of variables through learning algorithms and functional data analysis techniques. The second short term goal will focus on statistical analysis of extremes. I will investigate the limiting behavior of, and develop inference for, maxima of dependent risks such as insurance claims in a common portfolio which may be dependent due to common external factors. I will further study flexible max-id models for maxima in the medium regime for which the standard extreme-value theory does not apply. Machine learning will be used to study 0-1 patterns that arise in the context of extreme phenomena, such as floods or heatwaves. To help understand the causes of natural hazards and improve their forecasts, the third short-term goal is to study quantile treatment effects for high quantiles and structure learning algorithms for extremes. The proposed research program will significantly impact the way researchers assess risk in complex systems. The methodology for multivariate data and rare events that will be developed will allow to capture much more versatile dependence patterns and data structures than those accounted for by traditional statistical models. The research will make advances in extreme-value analysis, dependence modeling, and causal inference which are of interest to a wide statistical audience. The proposed methods will further lead to improved practices in insurance, risk management, and natural hazard forecasting. The results will be disseminated broadly through journal articles and talks in Canada and abroad; software will be made available to end-users through the R Project for Statistical Computing.