An intuitive rearranging of the Yates covariance decomposition for probabilistic verification of forecasts with the Brier score
This paper proposes a simple algebraic rearrangement of the Yates covariance decomposition for the Brier score that decomposes forecast error into three non-negative terms—variance mismatch, correlation deficit, and calibration-in-the-large—thereby making the conditions for optimal probabilistic forecasting transparent.