Last updated: March 2, 2026 by Dr. David Park

Bayesian Probability for Diagnostic Testing

Formula

Posterior = (Sensitivity * Prior) / (Sensitivity * Prior + (1 - Specificity) * (1 - Prior))

Bayesian probability updates prior beliefs using test characteristics (sensitivity and specificity) to calculate the probability of a condition given a positive or negative test result.

This approach is critical in medicine, where the positive predictive value of a test depends heavily on the prevalence of the condition in the population being tested.

Common use cases:

  • Medical test interpretation
  • Screening program evaluation
  • Risk assessment with imperfect information

Frequently Asked Questions

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Dr. David Park

Applied Mathematician, PhD Mathematics

David holds a PhD in Applied Mathematics from MIT. He has published research on numerical methods and computational algorithms used in engineering and scientific calculators.

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