Resolution and discrimination - two sides of the same coin

The notions of resolution and discrimination of probability forecasts are revisited. It is argued that the common concept underlying both resolution and discrimination is the dependence (in the sense of probability theory) of forecasts and observations. More specifically, a forecast has no resolution if and only if it has no discrimination if and only if forecast and observation are stochastically independent. A statistical tests for independence is thus also a test for no resolution and, at the same time, for no discrimination. The resolution term in the decomposition of the logarithmic scoring rule, and the area under the Receiver Operating Characteristic will be investigated in this light.