Bayesian Prior Calculator
Apply Bayes' theorem to update a prior probability given test sensitivity and false positive rate. Calculate the posterior probability after a positive or negative result.
Inputs
Results
Posterior P(A | positive test)
0.16
Posterior P(A | negative test)
0
How to Use This Calculator
- Enter the Prior Probability — your belief that the condition is present before seeing the test result (e.g., disease prevalence).
- Enter the Sensitivity (true positive rate) — the probability the test is positive given the condition is present.
- Enter the False Positive Rate — the probability the test is positive when the condition is absent (1 − Specificity).
- Bayes' theorem updates the prior: P(condition | positive test) = (sensitivity × prior) / P(positive test).
- The Posterior Probability is the updated belief after a positive result; it depends heavily on the prior.
- Low prevalence dramatically reduces the positive predictive value even for highly sensitive tests — this is the base rate fallacy.
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