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Bayes and the medical test

Write posterior(prior, sensitivity, specificity) returning P(sick | positive) rounded to 4 decimal places. Print it for prior 0.01, sensitivity 0.9, specificity 0.9.

Learn

A test that is right 90% of the time sounds reliable, yet if only 1 person in 100 has the condition, most positive results are false alarms. Bayes' rule combines the three numbers: P(sick | positive) = prior × sensitivity ÷ (prior × sensitivity + (1 − prior) × (1 − specificity)). Picture 1,000 people: 10 are sick (9 test positive), 990 are healthy (99 test positive anyway), so only 9 of 108 positives are truly sick.

Your task

Write posterior(prior, sensitivity, specificity) returning P(sick | positive) rounded to 4 decimal places. Print it for prior 0.01, sensitivity 0.9, specificity 0.9.

Stretch challenge

A second positive test on the same person: use the answer as the new prior. What do you get?

← Given that…The binomial distribution →

Python

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Practise the idea

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Bayes and the medical test: common questions

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