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Statistical extreme value theory is concerned with the use of asymptoticallymotivated models to describe the extreme values of a process. A number ofcommonly used models are valid for observed data that exceed some highthreshold. However, in practice a suitable threshold is unknown and must bedetermined for each analysis. While there are many threshold selection methodsfor univariate extremes, there are relatively few that can be applied in themultivariate setting. In addition, there are only a few Bayesian-based methods,which are naturally attractive in the modelling of extremes due to datascarcity. The use of Bayesian measures of surprise to determine suitablethresholds for extreme value models is proposed. Such measures quantify thelevel of support for the proposed extremal model and threshold, without theneed to specify any model alternatives. This approach is easily implemented forboth univariate and multivariate extremes.

Bayesian threshold selection for extremal models using measures of surprise