Bayes Theorem Calculator

What this tool does

Calculate bayes theorem using your data. A rare condition with an imperfect test produces mostly false positives — that is why a 90%-accurate test on a 1%-prevalence condition gives a posterior near 15%, not 90%.

How to use the Bayes Theorem Calculator

1. Enter or select prior probability p(a) (%).
2. Enter or select p(evidence | a) — sensitivity (%).
3. Enter or select p(evidence | not a) — false-positive rate (%).
4. Read the calculated result; change any measurement to compare alternatives.

Formula

P(A|B) = P(B|A)·P(A) / [ P(B|A)·P(A) + P(B|not A)·P(not A) ]

prior

Prior probability P(A) (%)

sens

P(evidence | A) — sensitivity (%)

fpr

P(evidence | not A) — false-positive rate (%)

A rare condition with an imperfect test produces mostly false positives — that is why a 90%-accurate test on a 1%-prevalence condition gives a posterior near 15%, not 90%.

Worked example

For bayes theorem calculator, the following measurements illustrate the exact method: Prior probability P(A) (%): 1; P(evidence | A) — sensitivity (%): 90; P(evidence | not A) — false-positive rate (%): 5.

Results explained

Posterior P(A | evidence) (%)

Posterior P(A | evidence) (%) from the formula above. A rare condition with an imperfect test produces mostly false positives — that is why a 90%-accurate test on a 1%-prevalence condition gives a posterior near 15%, not 90%.

Total probability of the evidence (%)

Total probability of the evidence (%) from the formula above. A rare condition with an imperfect test produces mostly false positives — that is why a 90%-accurate test on a 1%-prevalence condition gives a posterior near 15%, not 90%.

Prior odds

Prior odds from the formula above. A rare condition with an imperfect test produces mostly false positives — that is why a 90%-accurate test on a 1%-prevalence condition gives a posterior near 15%, not 90%.

Frequently asked questions