A0559
Title: Estimation of max-stable random fields using the periodogram for extreme events
Authors: Laleh Tafakori - RMIT University (Australia) [presenting]
Abstract: In recent years, there has been significant interest in the analysis of extreme events within stochastic processes. This has led to the exploration of various methodologies and techniques aimed at understanding and predicting extreme occurrences in both spatial and temporal domains. One approach involves the study of strictly stationary random fields with regularly varying marginal and finite-dimensional distributions. By exploiting the regular variation, the concept of the spatial extremogram is developed, which focuses specifically on the largest values present within the random field. Additionally, methods for estimating the corresponding extremal spectral density and its associated estimator, the extremal periodogram, have been devised. These existing procedures help in facilitating the analysis of extreme events and providing insights into their underlying characteristics. Furthermore, with advancements in computational capabilities, max-stable processes have become a cornerstone in the analysis of spatiotemporal extreme events. Simulation techniques play a crucial role in the inference of certain characteristics, particularly in spatial risk assessment for future events. An overview of existing procedures for simulating extreme events within stochastic processes is provided. By contextualizing these methodologies and comparing their theoretical properties, the aim is to enhance understanding and facilitate informed decision-making in the analysis of extreme events.
