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Name: Callum Barltrop

Talk Title: Novel diagnostic and uncertainty characterisation tools for multivariate return curves

Abstract: Risk measures that represent extremal probabilities are often used as summary statistics during statistical inference involving extreme value theory. In the univariate setting, arguably the most common measure is a return level; this is the value exceeded by a random variable with some user-specified probability p. However, little consideration has been given to extending this measure to the general multivariate setting. In this talk, we discuss one possible extension which we term a multivariate return curve. Similarly to return levels, these curves are defined, for a given probability p, to be all values of a multivariate random variable for which the joint survival probability is equal to p. For particularly small probabilities, these curves can be used to quantify the risk from extreme multivariate events and are often considered to be the natural multivariate extension to a return level. Moreover, for applications where the risk from combinations of two (or more) variables is considered important, such as the analysis of off-shore structures, these curves may allow resources to be better allocated than if the extremes of the variables were considered separately.  We also introduce novel diagnostic and uncertainty characterisation tools for return curve estimation and apply these methods to compare curve estimates from a range of multivariate extreme value models. Furthermore, we demonstrate our approach using a case study and illustrate some of the potential applications of return curves.

This talk is a contributed talk at EVA 2021.