Accounting for choice of measurement scale in extreme value modeling

TL;DR

This paper examines how the choice of measurement scale affects extreme value analysis and proposes a Bayesian method incorporating a Box--Cox transformation to improve inference and reduce bias, demonstrated on simulated and real wave data.

Contribution

It introduces a Bayesian approach with a Box--Cox transformation for scale uncertainty in extreme value modeling, enhancing inference accuracy.

Findings

Transforming scales affects tail behavior inference.

The proposed method improves convergence to extreme value limits.

Application to wave data demonstrates practical effectiveness.

Abstract

We investigate the effect that the choice of measurement scale has upon inference and extrapolation in extreme value analysis. Separate analyses of variables from a single process on scales which are linked by a nonlinear transformation may lead to discrepant conclusions concerning the tail behavior of the process. We propose the use of a Box--Cox power transformation incorporated as part of the inference procedure to account parametrically for the uncertainty surrounding the scale of extrapolation. This has the additional feature of increasing the rate of convergence of the distribution tails to an extreme value form in certain cases and thus reducing bias in the model estimation. Inference without reparameterization is practicably infeasible, so we explore a reparameterization which exploits the asymptotic theory of normalizing constants required for nondegenerate limit distributions. Inference is carried out in a Bayesian setting, an advantage of this being the availability of posterior predictive return levels. The methodology is illustrated on both simulated data and significant wave height data from the North Sea.