Precisión promedio y PR-AUC

Precision asks how many selected cases are positive. Recall asks how many of all positive cases have been selected. As a model's score threshold is lowered, more cases enter the selected set. Recall cannot decrease as the threshold is lowered, but precision can rise or fall depending on the newly included cases. A precision-recall curve traces this tradeoff. It is especially informative for a rare positive class because it directly exposes how many selected items are false alarms. A receiver operating characteristic curve answers a different question using the false-positive rate, whose denominator includes all actual negatives. Neither view removes the need to consider real decision costs. Average precision summarizes the precision-recall relationship by weighting precision values by the corresponding increases in recall. In a simple ranking without tied scores, it equals the average precision at the ranks occupied by positive cases. Suppose the only two positives appear first and third. The precisions at those positions are one and two-thirds, so average precision is about 0.833. The label PR-AUC can be ambiguous. Some reports mean trapezoidal integration of precision against recall; others use it loosely for average precision. Scikit-learn distinguishes average_precision_score from auc, which applies the trapezoidal rule. These values can differ because the interpolation assumptions differ. State the actual calculation. Precision depends on the prevalence of positives in the evaluation population. A score from a balanced sample may not describe a deployment setting where positives are rare. Report the positive fraction and evaluation design. Finally, a summary across thresholds does not select an operating threshold. Inspect the precision, recall and workload at the point where the model will actually be used.