Assessing the calibration of high-dimensional ensemble forecasts using rank histograms

TL;DR

This paper introduces new methods for evaluating the calibration of high-dimensional ensemble forecasts by mapping multivariate data to a univariate rank histogram, enabling effective detection of miscalibration.

Contribution

It proposes two novel multivariate ranking techniques—average ranking and band depth ranking—for assessing forecast calibration in high-dimensional settings.

Findings

Both ranking methods effectively detect miscalibration in simulations.

Methods scale efficiently to high-dimensional forecast data.

Case study confirms practical applicability for temperature forecasts.

Abstract

Any decision making process that relies on a probabilistic forecast of future events necessarily requires a calibrated forecast. This paper proposes new methods for empirically assessing forecast calibration in a multivariate setting where the probabilistic forecast is given by an ensemble of equally probable forecast scenarios. Multivariate properties are mapped to a single dimension through a pre-rank function and the calibration is subsequently assessed visually through a histogram of the ranks of the observation's pre-ranks. Average ranking assigns a pre-rank based on the average univariate rank while band depth ranking employs the concept of functional band depth where the centrality of the observation within the forecast ensemble is assessed. Several simulation examples and a case study of temperature forecast trajectories at Berlin Tegel Airport in Germany demonstrate that both multivariate ranking methods can successfully detect various sources of miscalibration and scale efficiently to high dimensional settings.