Data-based analysis of extreme events: inference, numerics and applications
Staff - Faculty of Informatics
You are cordially invited to attend the PhD Dissertation Defense of Olga KAISER on Monday, January 12th 2015 at 13h00 in room 006 (Informatics building)
The concept of extreme events describes the above average behavior of a process, for instance, heat waves in climate or weather research, earthquakes in geology and financial crashes in economics. It is significant to study the behavior of extremes, in order to reduce their negative impacts. Extreme value analysis (EVA), based on Extreme Value Theory, provides the necessary statistical tools.
Based on EVA and the Finite Element Time Series Analysis Methodology (FEM), this thesis introduces a semiparametric, nonstationary and non-homogenous framework for statistical regression analysis of spatio-temporal extremes. The resulting FEM-BV-EVA approach goes beyond a priori assumptions of standard methods based, for instance, on Bayesian statistics, Hidden Markov Models or Local Kernel Smoothing. The multivariate/spatial extension of FEM-BV-EVA describes the underlying spatial variability by the model parameters, referring to hierarchical modeling. The spatio-temporal behavior of the model parameters was approximated by locally stationary models and a nonparametric spatial nonstationary switching process.
The FEM-BV-EVA framework is computationally efficient as it deploys gradient free MCMC based optimization methods and numerical solvers for constrained, large, structured quadratic and linear problems. In order to demonstrate its performance, FEM-BV-EVA was applied to various test-cases and real-data and compared to standard methods. It was shown that parametric approaches lead to biased results if significant covariates are unresolved. Comparison to nonparametric methods based on smoothing regression revealed their weakness, the locality property and the inability to resolve discontinuous functions. Spatial FEM-BV-EVA was applied to study the dynamics of extreme precipitation over Switzerland. The analysis identified among others three major spatially dependent regions.
- Prof. Illia Horenko, Università della Svizzera italiana, Switzerland (Research Advisor)
- Prof. Rolf Krause, Università della Svizzera italiana, Switzerland (Internal Member)
- Prof. Igor Pivkin, Università della Svizzera italiana, Switzerland (Internal Member)
- Prof. Rupert Klein, Freie Universität Berlin, Germany (External Member)
- Prof. Simone Padoan, Bocconi University of Milan, Italy, (External Member)
- Prof. Olivia Romppainen, University of Bern, Switzerland (External Member)