Extreme quantile regions are spaces in which future extreme events can occur with a given low probability and most likely beyond the range of the observed data. The estimation of such regions is an important task in the analysis of extremes of many environmental phenomena such as wind speed, precipitation, pollution etc. Existing estimation methods are available but limited since they are unable to provide any measures of uncertainty. We develop univariate and bivariate schemes for estimating quantile regions under the Bayesian paradigm that outperforms existing approaches and provides natural measures of quantile region estimate uncertainty. The performance of the proposed methodology is examined on synthetic datasets. We illustrate the applicability of the proposed method by analyzing high bivariate quantiles for pairs of air pollutants, conditionally on different temperature gradations, recorded in Milan, Italy.
Invited talk in the session Multivariate Extremes, organised by Prof. M. Flak. Other presenters: C. Klueppelberg, A. Janssen, J. Segers.