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Bayes Factor Calculator

Calculate a Bayes factor to compare the evidence for two hypotheses.

About Bayes Factor Calculator

The Bayes factor quantifies how much the data shift belief between two hypotheses, independently of the prior. Unlike a p-value it can provide evidence for the null rather than merely failing to reject it. A Bayes factor below one is positive evidence for the null, which no p-value can ever express.

Formula

Bayes Factor

BF₁₀ = P(data | H₁) ÷ P(data | H₀); posterior odds = prior odds × Bayes factor

Bayes factor
Relative evidence the data provide for one hypothesis over another
posterior odds
Prior odds updated by the evidence

Worked example

With the default values below, Bayes Factor Calculator returns Bayes Factor of 4.00000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Likelihood under hypothesis 1minimum 0
0.08
Likelihood under the baseline hypothesisminimum 0
0.02
Prior odds for hypothesis 1minimum 0
1

Results

Bayes Factor
4.00000
Posterior Odds
4.00000
Posterior Probability of Hypothesis 1
80.000%
Strength of Evidence
Moderate evidence
Logarithm of the Bayes Factor
0.60206

Step by step

  1. 1Values used
  2. 2Bayes Factor
  3. 3Bayes Factor= 4.00000
  4. 4Posterior Odds= 4.00000
  5. 5Posterior Probability of Hypothesis 1= 80.000
  6. 6Strength of Evidence= Moderate evidence
  7. 7Logarithm of the Bayes Factor= 0.60206

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Bayes Factor calculated?

BF₁₀ = P(data | H₁) ÷ P(data | H₀); posterior odds = prior odds × Bayes factor The Bayes factor quantifies how much the data shift belief between two hypotheses, independently of the prior. Unlike a p-value it can provide evidence for the null rather than merely failing to reject it.

Why does Bayes Factor matter?

A Bayes factor below one is positive evidence for the null, which no p-value can ever express.

What values do I need to enter?

This calculator takes 3 inputs: Likelihood under hypothesis 1, Likelihood under the baseline hypothesis, Prior odds for hypothesis 1. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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