F1 Score vs PR Curve If I understood correctly, PR Curve it's just the mean of F1 score computed multiple times with different thresholds.
In the task of outlier detection those are two suggested metrics given the fact that the datasets are highly inbalanced.
My question is, if I know in advance the contamination factor (the percetange of the anomalies) of a dataset, should I use directly the F1 Score instead of the PR Curve?
If I were to give my self an answer, I would say yes because knowing the contamination factor gives me the right threshold value and so it's useless to compute the PR Curve.
Does it make sense or am I wrong?
 A: The PR curve is not "the mean of the $F_1$ score computed multiple times with different thresholds". Both use Precision and Recall values to be computed but that does not mean they reflect similar information. The most obvious difference is that the PR curve has a baseline value while the $F_1$ score does not. (See What is "baseline" in precision recall curve for more details.)
Now, for your main question: These are multiple ways of defining an anomaly/outlier. If these anomalies/outliers are real data, they should be included in all our calculations (e.g. we aim to predict body weight and we have an instance of an adult male weighing 46 kg), if these anomalies/outliers are corrupted data (e.g. in the same prediction problem as above but we have an instance of an adult male weighing 8.4 kg) it makes sense to remove them from subsequent calculations. In the first case, we have very large but expected variability but in the latter an obviously wrong recording. Our model needs to have robustness against unusual instances. It is the corrupted instances we can "safely exclude". That said, we need to incorporate clearly that pre-processing in our pipeline and report it. This filtering step is part of our analysis! In any case, we should not throw away the "outliers" before determining why there are "outlying".
The fact that we know that approximately $x$% of our data is going to be corrupted (not "just" anomalies/outliers), does mean we need to account for them in our overall analysis pipeline but that does not mean we have to beautify our metrics for them.  After our filtering steps, the PR curve and/or $F_1$ score calculations should continue as normal. This allows us to have consistent and comparable metrics of our model's performance.
To conclude, PR curve and $F_1$ are both informative in the presence of anomalies. We should make it explicit how we account for them and then calculate our metrics in a consistent and documented manner.
