Unlike traditional point forecasts that predict a single expected value, a distributional forecast provides a probability distribution over a range of possible outcomes. This allows for a more nuanced understanding of uncertainty.

What is a Coverage Score?

A coverage score measures how well a distributional forecast captures the actual observed values. Here's the idea:

• Nominal Coverage: You choose a desired coverage probability (e.g., 90%, 80%).
• Prediction Intervals: The distributional forecast generates prediction intervals (ranges) around its predictions, determined by the chosen coverage probability.
• Evaluation: The coverage score is the percentage of times the actual observed values fall within the predicted intervals.

Interpretation

• Ideal Coverage: In an ideal scenario, your coverage score aligns with the nominal coverage. A 90% coverage score implies that 90% of the time, the real values fall within the prediction intervals.
• Underconfident Forecasts: If your coverage score is consistently higher than the nominal coverage, it suggests your prediction intervals are too wide – your model is overly uncertain.
• Overconfident Forecasts: If your coverage score is consistently lower than nominal coverage, your prediction intervals are too narrow. Your model underestimates uncertainty.

Real Use Cases

Coverage scores are important in several risk-sensitive scenarios:

• Financial Risk Management: Assessing the likelihood of different portfolio return scenarios in stock market predictions, where understanding the distribution of potential outcomes is crucial for planning.
• Supply Chain Optimization: Forecasting sales or demand with distributional forecasts and accurate coverage scores allows for stock-out risk management and inventory planning.
• Weather Forecasting: Understanding the full range and probability of different rainfall or temperature scenarios with adequate coverage is essential for planning in agriculture or event planning.

Inferences

Coverage scores help you:

• Evaluate Model Performance: They go beyond simple accuracy metrics to assess how well your model captures uncertainty.
• Calibration: If coverage scores deviate from the expected values, you may need to calibrate your forecasts.
• Decision-Making: Accurate coverage scores aid risk-informed decision-making in areas where understanding the full range of possible outcomes is vital.