Parametric multi-fidelity Monte Carlo estimation with applications to extremes

TL;DR

This paper develops and compares multi-fidelity parameter estimation methods for extreme value models, leveraging both high- and low-fidelity data to improve efficiency in modeling rare events.

Contribution

It introduces and evaluates three multi-fidelity estimation techniques specifically for parametric models in extreme value analysis, including practical applications.

Findings

Multi-fidelity methods improve estimation efficiency for extreme value models.

Joint maximum likelihood outperforms other methods in certain scenarios.

Application to ship motion extremes demonstrates practical benefits.

Abstract

In a multi-fidelity setting, data are available from two sources, high- and low-fidelity. Low-fidelity data has larger size and can be leveraged to make more efficient inference about quantities of interest, e.g. the mean, for high-fidelity variables. In this work, such multi-fidelity setting is studied when the goal is to fit more efficiently a parametric model to high-fidelity data. Three multi-fidelity parameter estimation methods are considered, joint maximum likelihood, (multi-fidelity) moment estimation and (multi-fidelity) marginal maximum likelihood, and are illustrated on several parametric models, with the focus on parametric families used in extreme value analysis. An application is also provided concerning quantification of occurrences of extreme ship motions generated by two computer codes of varying fidelity.