Conditional Probability - Theory & Concepts - Engineering Data Analysis Diagnostic Testing

Understanding how probabilities change when new information is available, including Bayes' Theorem and Independence.

Bayes' Theorem in Diagnostic Testing

Prevalence

P(D)

10%

Sensitivity

P(+\mid D)

90%

Specificity

P(-\mid D^c)

90%

Population Grid (N = 100)

True Positive (TP: 9)

False Negative (FN: 1)

False Positive (FP: 9)

True Negative (TN: 81)

PPV (Post-test prob of disease | positive test)

50.0%

P(D\mid +) = \frac{P(+\mid D)P(D)}{P(+\mid D)P(D) + P(+\mid D^c)P(D^c)}

NPV (Post-test prob of healthy | negative test)

98.8%

P(D^c\mid -) = \frac{P(-\mid D^c)P(D^c)}{P(-\mid D^c)P(D^c) + P(-\mid D)P(D)}

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