Detection
Precision and Recall
Precision = TP / (TP+FP)
Recall = TP / (TP+FN)
F-Score = 2/(1/P+1/R) (harmonic mean of P and R
ROC Curve:
when moving the decision boundary to increase the detection rate, false alarm rate also increases. So the area under ROC curved to judge how good the model is.

Practical Challenge: Unknown Likelihood
To have d good detection model, a precise mathematical model for the likelihood is required. In many practical cases it is difficult, so learning based approach (Pattern Recognition) becomes a good alternative.