What does the receiver operating characteristic (ROC) curve illustrate?

The receiver operating characteristic (ROC) curve is a graphical representation that illustrates the relationship between the true positive rate (TPR) and the false positive rate (FPR) at various threshold settings. The true positive rate, also known as sensitivity or recall, measures the proportion of actual positives that are correctly identified by the model, while the false positive rate measures the proportion of actual negatives that are incorrectly classified as positives.

When examining this relationship, the ROC curve allows practitioners to visualize how well their binary classification model distinguishes between the positive and negative classes as the threshold for making classifications is varied. The area under the ROC curve (AUC) can also be used as a single scalar value to evaluate the model's performance, with a higher AUC indicating better performance across different threshold settings.

The other options provided focus on different aspects of model evaluation that do not directly pertain to the ROC curve itself. The distribution of predicted probabilities over classes reflects how predictions are spread out across potential outcomes but doesn't illustrate the TPR vs. FPR relationship. The accuracy of classification across different thresholds is relevant but is typically represented by the accuracy-recall or precision-recall curves rather than the ROC curve. Similarly, the comparison of precision and recall relates to the trade-offs between