Sequence / Objectives
verifiedProbabilistic Forecasting
A single predicted number is almost never what a decision needs. Stocking a warehouse needs to know how bad the bad case is; scheduling a grid needs the same. Probabilistic forecasting predicts a distribution rather than a point, and the useful part is usually the width rather than the middle.
Train against a likelihood or a quantile loss rather than squared error, and evaluate with a proper scoring rule — CRPS or pinball — because RMSE on the median rewards a confidently wrong forecast the same as a hedged one. Calibration is the property that matters and is checked separately from sharpness: intervals should contain the truth as often as they claim, and the narrowest calibrated interval is the goal.
Predict p(y sub t+h | y sub 1:t ) and score it with CRPS = ∫ (F(z) − 1{z ≥ y})² dz, which is minimised only by the true distribution. Uncertainty grows with h because errors compound, so a well-calibrated model's intervals must widen with the horizon — an interval that does not widen is miscalibrated somewhere, whatever its coverage on average says.
16 values. The left group decays steeply; the right group is 36% of the way to flat, and reads flatter than the left.
The predictive distribution over outcomes, one step ahead and further out. Drag the horizon up to watch it spread toward uninformative — an interval that fails to widen with distance is miscalibrated, whatever its average coverage reports.
Reviewed by opendroid · 2026-08-18
- arXiv:1704.04110 — DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks