Compute and interpret quantile loss vs RMSE

Q: Compute and interpret quantile loss vs RMSE

This question evaluates competency in probabilistic forecasting evaluation, including understanding of quantile (pinball) loss versus point-error metrics like RMSE/MAE, calibration and empirical coverage of prediction intervals, and decision-making under asymmetric costs.

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Quantile (Pinball) Loss vs RMSE/MAE; Computations and Calibration

You are evaluating probabilistic forecasts for a time series/ML regression task. You have both point forecasts (e.g., median) and quantile forecasts (e.g., 90th percentile) produced out-of-sample.

Tasks

Define the quantile (pinball) loss L_q(y, ŷ) for a quantile q and explain how it evaluates probabilistic forecasts differently from RMSE/MAE.
Given observations y = [100, 120, 90] and predicted 90th-percentile forecasts at q = 0.9, ŷ_q = [110, 115, 95], compute the average pinball loss.
Given median forecasts ŷ_0.5 = [102, 118, 93], compute the RMSE.
If underprediction is more costly than overprediction (asymmetric costs), decide which model you would prefer and justify.
Describe methods to assess calibration and empirical coverage of 80% and 90% prediction intervals.

Compute and interpret quantile loss vs RMSE

Quantile (Pinball) Loss vs RMSE/MAE; Computations and Calibration

Tasks

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Compute and interpret quantile loss vs RMSE

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Quantile (Pinball) Loss vs RMSE/MAE; Computations and Calibration

Tasks

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