Bayes Update

Update a prior probability with new evidence using a likelihood ratio.

Mode

Prior Scale

Prior Probability

Likelihood Ratio (LR)

Sensitivity (0-100)

Specificity (0-100)

Observation Result

How it works

Choose a mode first:

Likelihood ratio mode (LR): use this if you already have LR for the evidence.
Sensitivity and specificity mode: use this if you have a test like signal with sensitivity and specificity.

Then enter:

Prior probability: your base rate before new information.
In LR mode: enter Likelihood ratio (must be greater than 0).
In Sensitivity and specificity mode: Sensitivity and specificity (0-100).
Result: Positive or Negative, the calculator will use LR+ or LR- automatically.

Posterior probability: updated probability after accounting for the evidence.
Prior odds and posterior odds: shown to make the update transparent.
LR used: the evidence strength that drove the update.

Prior 50%, LR 2 → posterior about 66.67%.
Prior 20%, LR 3 → posterior about 42.86%.

Prior cannot be exactly 0% or 100% in Bayes updates because odds become undefined. Use realistic priors, even if they are very small or very large.