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Bayesian probability worksheet

Update a belief with evidence, the way a tax form adds up numbers: fill in the underlying quantities (white boxes) and the derived ones (shaded boxes) compute themselves. An interactive version of the 2022 worksheet. Any prior or likelihood can be edited as a probability or as odds — the linked boxes follow along.

Hypotheses & prior

1
Null hypothesis H0the default / status quo
2
Alternative hypothesis H1the claim under test
3
Prior P(H0)how likely H0 seems before the evidence
4
Prior P(H1)how likely H1 seems before the evidence
5
Prior odds
P(H1) : P(H0)

Evidence

6
New information E
7
Likelihood P(E | H0)chance of E if H0 holds
8
Likelihood P(E | H1)chance of E if H1 holds
9
Likelihood ratio
Box 8 ÷ Box 7
—

Conclusion

10
Posterior odds
Box 5 × Box 9
—
11
Posterior P(H0 | E)
1 ÷ (1 + Box 10)
—
12
Posterior P(H1 | E)
Box 10 ÷ (1 + Box 10)
—
The same update, as natural frequencies
Weight of evidence (log-odds · decibans)
When is this worksheet reliable?

The update is only as trustworthy as its inputs. It becomes highly unreliable when the alternative hypothesis H1 is left vague rather than precisely specified, or when the evidence E is filtered — for instance if a source reports only the facts favourable to one hypothesis. It works well when you are confident that all relevant information, both for and against H1, is being reported.

Entering a range (e.g. 0.03–0.07, or 0.05 ± 0.02) in any box shows how far the conclusion moves as the assumption varies.

Enter numbers as decimals or percentages (0.02 or 2%), as odds (16 or 16:1 in Box 5), or as ranges. The applet source is released under the MIT license; the mathematical content is reserved.