Ensemble recall function equivalence

Background: The true Fire Danger Index (FDI) is a latent variable that machine learning models attempt to estimate as a noisy prediction. Model ensembles are used to create a more robust estimate by averaging predictions.

Question / Future Work: It is an open question whether the mathematical relationship between the nonlinear function used to calculate recall (the percentage of fires correctly identified) and the ensemble-averaged FDI map is trivial, specifically whether the average recall across ensemble members is mathematically equivalent to the recall calculated from the ensemble-averaged FDI map.

Why It Matters: Understanding this relationship is key to rigorously validating the performance gains of ensemble averaging over individual model predictions when evaluation relies on a non-linear metric like recall.

Evidence: The recall is a nonlinear function of the ground truth and the FDI; therefore, Equation 1 is not trivial. This implies that most members are equally confident in labeling fire and no-fire events.