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

TL;DR

This paper introduces a Bayesian-like method for predicting extreme values that preserves probability, comparing it with a Frequentist approach, and demonstrating their reasonable agreement.

Contribution

It presents a noninformative Bayes-like approach for probability-preserving extreme prediction, extending previous Frequentist methods and analyzing their correspondence.

Findings

Bayes-like and Frequentist approaches show good agreement

The methods effectively predict extreme tail events

The approach offers a probabilistically consistent prediction framework

Abstract

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.