A bias-corrected decomposition of the Brier score

Abstract

The Brier score is a widely used measure of performance for probabilistic forecasts of event occurrences and is often decomposed additively into three terms that quantify the reliability and resolution of the forecasts and the uncertainty of the forecast events. The standard decomposition yields biased estimates of the large-sample values of these three quantities: reliability is overestimated and uncertainty is underestimated, while resolution may be either overestimated or underestimated. An unbiased decomposition is shown to be unattainable but a new decomposition is proposed that has smaller biases and therefore provides a more accurate measure of forecast performance. The implications for the Brier skill score and the attributes diagram are discussed and results are illustrated with seasonal forecasts of sea-surface temperatures.