Bayes Practice

Bayes Practice

Part 1: COVID-19 Rapid Antigen Test

You’re using a COVID-19 rapid antigen test during a period when the local infection rate is 8% (meaning 8 out of every 100 people in your community currently have COVID-19). Based on real clinical studies, this type of rapid antigen test has an average sensitivity of 69.3% and specificity of 99.3%.

You take the test and it comes back positive. What is the probability that you actually have COVID-19?

Given information:

• Prior probability (prevalence): P(COVID+) = 0.08

• Sensitivity: P(Test+

  COVID+) = 0.693

• Specificity: P(Test-

  COVID-) = 0.993

Part 2

Why is “What is the probability that you actually have COVID-19?” a stupid, bad and wrong question and yet this is how experts talk.