What can the data scientist reasonably conclude about the distributional forecast related to the test set?
The coverage scores indicate that the distributional forecast is poorly calibrated. These scores should be approximately equal to each other at all quantiles.
The coverage scores indicate that the distributional forecast is poorly calibrated. These scores should peak at the median and be lower at the tails.
The coverage scores indicate that the distributional forecast is correctly calibrated. These scores should always fall below the quantile itself.
The coverage scores indicate that the distributional forecast is correctly calibrated. These scores should be approximately equal to the quantile itself.
Explanations:
The coverage scores should not be approximately equal at all quantiles. It is expected that coverage may vary at different quantiles, with higher quantiles having higher coverage, indicating more uncertainty.
Coverage scores do not necessarily peak at the median and lower at the tails. The distribution may be properly calibrated even if coverage is not symmetric across quantiles.
Coverage scores do not need to fall below the quantile itself. The coverage score at a specific quantile should ideally represent the proportion of actual values that lie below the forecasted quantile.
The coverage scores should approximately match the quantile values, indicating that the forecast is calibrated. A coverage of 0.489 at the 0.5 quantile and 0.889 at the 0.9 quantile suggests correct calibration.
I evaluate that the answer is:
The coverage scores indicate that the distributional forecast is correctly calibrated. These scores should be approximately equal to the quantile itself.