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Title: Modelling non-stationarity in bivariate hazard curves Authors:  Callum Barltrop - Lancaster University (United Kingdom) [presenting]
Abstract: Multivariate hazard curves are defined, for a given probability $p$, as 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 assess the risk of extreme multivariate events and are often considered to be the natural multivariate extension to a return level. Furthermore, for applications where the risk from combinations of two (or more) variables is considered important, these curves may allow resources to be better allocated. However, difficulties arise when considering environmental data (temperature, wind speed, etc.) since such processes often exhibit non-stationarity. This feature means the underlying hazard curves will also be non-stationary, varying following underlying physical processes and potentially other external factors. We show how to capture non-stationarity in both the margins and dependence structures of bivariate datasets using a previous extension of the model. We then apply this theory to obtain estimates of non-stationary bivariate hazard curves and illustrate the effectiveness of our approach using a simulation study. Moreover, we further demonstrate our approach using data from the 2018 UK Climate Projections (UKCP18) and discuss potential avenues for future research.