Bayes Theorem Calculator: Base Rates and Diagnostic Testing
Use base rate, sensitivity, and specificity to see posterior probability through natural frequencies.
At a glance
- Computes
- Posterior probability after a positive or negative result, shown as natural frequencies.
- You supply
- Base rate, sensitivity, specificity, and a population size.
- Use when
- You need to see why a positive test for a rare condition often misleads.
- Not for
- Updating on several dependent pieces of evidence at once.
Probability condition is present after a positive signal
Ready
Default rates create many false positives.
- Absent after a negative signal
- 100.0%
- Positive signals that are true
- 99 of 594
- Simulated PPV
- Not run
| Cell | Expected count |
|---|
Run the simulation to fill Monte Carlo metrics and convergence.
Positive predictive value against Trial; reference at Exact Bayesian PPV
| Trial | True positives | Positive signals | Simulated PPV |
|---|
PPV = sensitivity * base rate / total positive-signal probability
How?
How this is calculated
Positive predictive value uses Bayes theorem and the law of total probability. Natural frequencies show true positives and false positives in the same population size so the denominator is visible.
Formula: PPV = sensitivity * base rate / total positive-signal probability
Sources
- StatLect Bayes rule. StatLect. Retrieved .
- Positive and negative predictive values. Wikipedia. Retrieved .
Method last reviewed