A Noninformative Bayes-like Approach to Probability-Preserving Prediction of Extremes

The extrapolation of extremes to values beyond the span of stationary univariate historical data is considered from Bayesian and Frequentist perspectives. The intention is to make predictions which in some sense "preserve probability". A Frequentist approach based on a simple curve-fit estimate of the tail parameter $\xi$ of a Generalised Pareto Distribution was described in McRobie (2014) (arXiv:1408.1532). In this paper, the corresponding Bayes-like approach is described, using a plausible noninformative prior for the tail parameter. The two approaches, though philosophically different, show a reasonable degree of correspondence.