Abstract
Many types of extreme events in nature elicit their impact from the occurrence of a cluster of extreme values, that is, when several extremely large or small values are observed within a short period. This course will cover an overview of the theory and statistical analysis of extremes of stationary time-series. Under certain dependence conditions it can be shown that the exceedances of the levels by the random variables in the series take on the character of a Poisson process. This character lends itself to a wide range of asymptotic distributional results for the largest values of a time-series, which can be exploited for statistical inference.
Day 2: will cover refined characterizations of the probabilistic behavior of a stationary time-series by focusing on renormalized Markov processes that are conditioned to attain an extreme event, subject to the level of the extremity tending to the upper end point of the marginal distribution. Under a common theme for handling different extremal dependence types, the course will explore the conditional approach to time series extremes and will present an overview of sampling based methods for estimating key quantities of interest.
Modelling will involve the development of extreme value statistical models and their application to data sets taken from financial and environmental applications.
Brief Biography
Ioannis Papastathopoulos received his undergraduate training in Statistics and Insurance Science at the University of Piraeus. He received his MSc in Statistics and PhD in Statistics from Lancaster University. He held a Brunel Research Fellowship at the School of Mathematics, University of Bristol, and a Chancellor's Fellowship in Statistics at the School of Mathematics, University of Edinburgh. Since 2019, he has been a Lecturer in Statistics at the School of Mathematics, University of Edinburgh. Ioannis has interests in both theoretical and applied aspects of multivariate extreme value theory and works at the interface between applied probability and statistics.