helpmedecide

Bayesian calculator.

A positive test isn't an answer — it's an update. Bayes' theorem turns your prior belief and the strength of each signal into the only number that matters: how likely it is now.

How it works01
  1. 1
    Set your prior — How likely was the hypothesis before any evidence?
  2. 2
    Add each signal you've seen — For each one: how often it fires when the hypothesis is true vs. when it's false, and what you actually observed.
  3. 3
    Read the chain — Each signal updates your belief, and that becomes the prior for the next one.
  4. 4
    Read the posterior — The final probability after combining everything you've seen.
Worked examples02
Pick a worked example

Or start from any one and tune the numbers — they all snap to "Custom" once you adjust.

The classic. A 99%-accurate test for a 1-in-100 disease still leaves you well under coin-flip odds — because false positives swamp the few real cases.

Frame the question03

What's the claim?

The numbers04

Before any evidence, how likely is it that I have the disease?

%
Signal 01
What did you observe?

When I have the disease, what % of the time does the test comes back positive?

%

When the hypothesis is false, what % of the time does the test comes back positive?

%
The answer05
After a positive signal
16.67percent
chance the hypothesis is true

Even after the evidence, it's still unlikely — the evidence raises your belief, but not by much.

In plain language

Imagine 1,000 people in this situation. About 10 truly fit the hypothesis and trigger the signal (true positives), while about 50 don't fit but still trigger it (false positives). So out of about 60 total positive signals, only 10 are real — that's 16.7%.

100 people, by the numbers06

Each square is one person.

1 true positive
5 false positive
94 true negative
0 false negative (missed)
How to think about this07

A signal moves belief, doesn't reset it.

The base rate matters more than you think. A very accurate test for a very rare thing is still mostly false positives. Always start from the prior.
Update, don't replace. A signal moves your belief; it doesn't reset it. The posterior is the new prior the next time you see evidence.
Two numbers describe a test, not one. "99% accurate" usually means TPR. The FPR is what determines how often a positive is wrong.
Independence is an assumption. Chaining multiple signals assumes they're independent given the hypothesis. Two correlated signals (say, two doctors looking at the same scan) shouldn't be multiplied as if they were separate evidence.
On certainty: If the posterior is 60%, you have a slight lean — not a verdict. Use it to decide what to do next (a confirmatory test, more data, a smaller bet), not to declare the question settled.
Related essays99

From the notebook.

May 11, 2026

What a Positive Test Really Means

A 99% accurate test comes back positive. Most people assume they're 99% likely to have the disease. The real answer is closer to 9% — and the math is easier than it looks.