The first speaker is Simone Padoan (Bocconi University) and her presentation is entitled “Bayesian inference and prediction based on the Peaks Over Threshold method”. After the lunch break Anna Kiriliouk (Université de Namur) will give a talk on “Estimating probabilities of multivariate failure sets based on pairwise tail dependence coefficients”. The abstracts of both presentations are at the end of this post.
The seminar is from 12.00 till 14.20 (lunch included) in the NU Building, room NU-2A65. Address: De Boelelaan 1111, 1081 HV Amsterdam.
The EVTA-seminar series aims at inviting researchers in the field of Extreme Value Analysis from abroad and is jointly organized by four Dutch universities. The four Dutch universities collaborating in the EVTA seminar series are: Erasmus University Rotterdam, Vrije Universiteit Amsterdam, Tilburg University and University of Amsterdam. More information can be found on the EVTA website.
If you are interested in joining this seminar, please send an email to the secretariat of the Department of Econometrics and Data Science at secretariaateconometrie.sbe@vu.nl
Abstracts
“Bayesian inference and prediction based on the Peaks Over Threshold method” by Simone Padoan
In this work we focus on the Peaks Over Threshold (POT) method, which is arguably the most popular approach in the univariate extreme values literature for analysing extreme events. In this setting, we investigate a Bayesian inferential procedure with rigorous theoretical guarantees that allows to extrapolate extreme events in the very far of the tail of the data distribution with a simple uncertainty quantification. An important purpose in risk analysis is the prediction of future events that are more severe than those yet seen. Leveraging on the proposed Bayesian approach we derive a posterior predictive distribution that can be used for forecasting the size and occurrence of extreme events. We show that such a posterior predictive distribution is an accurate estimator of the true predictive distribution of extreme events.
“Estimating probabilities of multivariate failure sets based on pairwise tail dependence coefficients” by Anna Kiriliouk
Estimating the probability of extreme events involving multiple risk factors is a critical challenge in fields such as finance and climate science. We propose a semi-parametric approach to estimate the probability that a multivariate random vector falls into an extreme failure set, based on the information in the tail pairwise dependence matrix (TPDM) only. The TPDM provides a partial summary of tail dependence for all pairs of components of the random vector. We propose an efficient algorithm to obtain approximate completely positive decompositions of the TPDM, enabling the construction of a max-linear model whose TPDM approximates that of the original random vector. We also provide conditions under which the approximation turns out to be exact. Based on the decompositions, we can construct max-linear random vectors to estimate failure probabilities, exploiting its computational simplicity. The algorithm allows to obtain multiple decompositions efficiently. Finally, we apply our framework to estimate probabilities of extreme events for real-world datasets, including industry portfolio returns and maximal wind speeds, demonstrating its practical utility for risk assessment.