Clarification on the Definition and Source of Prediction Intervals

[Claire-bx]

I would like to confirm my understanding of how the prediction interval (e.g., pred 0.9) is defined and implemented in the model.

When setting pred 0.9, does it indicate that the true value is expected to fall within this interval with a probability of 90%?
Specifically, are the lower and upper bounds corresponding to the 5% and 95% quantiles of the predictive distribution?

Regarding the source of uncertainty in interval prediction:

By model uncertainty, I refer to cases where, even with the same input and fixed model parameters, the model output may vary due to stochastic components (e.g., dropout, sampling, or ensemble randomness).
By data uncertainty, I refer to the uncertainty learned from the data itself, where the model structure or parameterization is designed to capture aleatoric uncertainty and produce probabilistic outputs.

Could you please clarify which type(s) of uncertainty are considered in our implementation when generating the prediction intervals?

Your insights would be greatly appreciated.

[lostella]

@Claire-bx taking the 0.9 prediction gives you the 0.9 quantile: the true value is expected to fall below this level 90% of the time.

This is an estimate of the distribution width learned from the data: Chronos models obtain this via sampling, Chronos-Bolt models instead were trained with a quantile regression objective, so they output the quantile estimates directly.

[Claire-bx]

Chronos models obtain the quantiles via sampling. In that case, how can we distinguish whether the variation in the predicted quantiles is due to the model’s inherent stochasticity (e.g., sampling or instability) rather than genuine uncertainty learned from the data?

[lostella]

You can increase the number of sample paths drawn (default is 20) and that will give you more stable quantile estimates between runs.

Or you can use Chronos-Bolt models, that directly emit quantile estimates with no sampling involved: these will have no variation in the predicted quantiles.