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I want to report the AUROC and the AUPRC of a prediction model using an unbalanced dataset. Is it correct that I have to balance my data to calculate the AUROC but leave the data unbalanced to calculate the AUPRC?

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ROC curves are insensitive to class imbalance. This means that if you re-balance your data, you will obtain (statistically) the same ROC curve.

PR curves are sensitive to class imbalance, specifically to the baseline probability of positive events. If you calculate the AUPRC on a dataset which is not representative of the balance of your dataset, the AUPRC is meaningless.

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