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Could someone please clarify, whether it is appropriate to define a prediction interval or an equivalent for an RMSE and MAE measure. If so, could you please suggest how such an interval is defined.

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This doesn't really make sense. RMSE and MAE capture error in a model, while prediction intervals capture uncertainty in model predictions. So they are related to each other, in that higher error in the model will lead to greater uncertainty in model predictions. But it does not make sense to talk about the error in the uncertainty of a model prediction.

However, one can calculate the confidence interval of an error estimate such as RMSE.

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