医疗人工智能模型用于检测500名患者的疾病：

实际上有100名患者患有这种疾病
模型正确识别了其中70种
它错误地将50名健康患者诊断为患病

问题：

计算模型的精度。
计算型号的召回率。

Question

医疗人工智能模型用于检测500名患者的疾病：

实际上有100名患者患有这种疾病
模型正确识别了其中70种
它错误地将50名健康患者诊断为患病

问题：

计算模型的精度。
计算型号的召回率。

BlackTom AI · Accepted Answer

Precision (positive predictive value) = TP / (TP + FP). Recall (sensitivity) = TP / (TP + FN).

Relevant concepts:
- True Positive (TP): sick patients correctly identified = 70.
- False Positive (FP): healthy patients incorrectly labeled sick = 50.
- False Negative (FN): sick patients missed = actual sick − TP = 100 − 70 = 30.
- True Negative (TN): healthy correctly labeled healthy = total healthy − FP = (500 − 100) − 50 = 400 − 50 = 350.
Precision tells us of all predicted positives, what fraction are truly positive. Recall tells us of all actual positives, what fraction were found.

Step-by-step calculations (all intermediate steps shown):
1. Compute FP and FN explicitly:
   - FN = 100 − 70 = 30.
   - FP = 50 (given).
2. Precision = TP / (TP + FP) = 70 / (70 + 50) = 70 / 120.
   - 70 / 120 = 7 / 12 ≈ 0.583333...
   - Rounded to two decimal places = 0.58.
3. Recall = TP / (TP + FN) = 70 / (70 + 30) = 70 / 100 = 0.7.

Why the correct answer is correct:
- Precision calculation uses only predicted positives (TP + FP = 120) and counts how many of those are true (70), giving 70/120 ≈ 0.58.
- Recall uses actual positives (TP + FN = 100) and counts how many were detected (70), giving 70/100 = 0.7.

Why other common metrics would be incorrect here:
- Accuracy = (TP + TN) / total = (70 + 350) / 500 = 420/500 = 0.84, but the question asked for 精度 (precision) and 召回率 (recall), not accuracy.
- Specificity = TN / (TN + FP) = 350 / 400 = 0.875, also not asked.

Final confirmation: Precision = 0.58 and Recall = 0.70, which matches the provided answer [0.58, 0.7].

医疗人工智能模型用于检测500名患者的疾病：实际上有100名患者患有这种疾病模型正确识别了其中70种它错误地将50名健康患者诊断为患病问题：计算模型的精度。计算型号的召回率。单项选择题

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医疗人工智能模型用于检测500名患者的疾病： 实际上有100名患者患有这种疾病 模型正确识别了其中70种 它错误地将50名健康患者诊断为患病 问题： 计算模型的精度。 计算型号的召回率。单项选择题