On the Calibration of Multilevel Monte Carlo Ensemble Forecasts

TL;DR

This paper introduces a method to derive a statistically consistent ensemble forecast from multilevel Monte Carlo simulations, enabling comprehensive verification of forecast calibration using standard techniques.

Contribution

It proposes a simple algorithm to create a unified ensemble forecast from multilevel Monte Carlo hierarchies, facilitating evaluation of multiple statistics simultaneously.

Findings

Enables verification of forecast calibration using standard ensemble methods.

Provides a statistically consistent ensemble forecast from multilevel Monte Carlo hierarchies.

Facilitates evaluation of multiple statistics with a single ensemble.

Abstract

Multilevel Monte Carlo can efficiently compute statistical estimates of discretized random variables, for a given error tolerance. Traditionally, only a certain statistic is computed from a particular implementation of multilevel Monte Carlo. This paper considers the multilevel case when one wants to verify and evaluate a single ensemble that forms an empirical approximation to many different statistics, namely an ensemble forecast. We propose a simple algorithm that, in the univariate case, allows one to derive a statistically consistent single ensemble forecast from the hierarchy of ensembles that are formed during an implementation of multilevel Monte Carlo. This ensemble forecast then allows the entire multilevel hierarchy of ensembles to be evaluated using standard ensemble forecast verification techniques. We demonstrate the case of evaluating the calibration of the forecast in this paper.