ROC and PR curves are primarily visual tools to select a given operating point (cutoff) of existing models for the task at hand (high recall, precision, ...). Area under either curve is a commonly used, though not very intuitive, summary statistic of the performance of models over their entire operating range.

In my opinion, AUC is useful as a scoring function in hyperparameter search, or for studies that compare the performance of different learning methods (e.g. where you don't want to examine a specific operating point). That said, AUC is far less practical to finally select a model to be used for a specific task and it is entirely irrelevant to select the model's operating point. It is perfectly possible for a suitable model for a given task to have terrible AUC under either curve. 


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**Example**

Suppose I want very high precision but don't need a lot of recall and I have two models $A$ and $B$ with corresponding PR curves (precision as function of recall):
$$
\begin{align}
PR_A(r) &= e^{-2r} \quad \rightarrow \quad \text{PR-AUC} \approx 0.43\\
PR_B(r) &= 0.8 \quad \rightarrow \quad \text{PR-AUC} = 0.80
\end{align}
$$
The precision of model $A$ is higher than $B$ up to about $11\%$ recall. Its AUC is far worse, though. Given the application I presented, model $A$ is probably the best choice. Examples of such applications:

 - **gene prioritization**: rank genes based on association with diseases; the top ranked genes are likely to become targets for (expensive) biological analyses.
 - **fraud detection**: rank transactions based on potential of fraudulence; top ranked transactions may lead to lawsuits, false positives lead to counterclaims.