Bayes Factor Calculator for R

Formula Used

Direct evidence: BF10 = P(data | H1) / P(data | H0)

Likelihood ratio: BF10 = L(H1) / L(H0)

Odds method: BF10 = posterior odds / prior odds

BIC approximation: BF10 ≈ exp((BIC0 - BIC1) / 2)

The calculator also computes BF01, natural log BF10, log10 BF10, prior odds, posterior odds, and posterior probability for H1.

Example Data Table

How to Use This Calculator

1. Select the calculation method that matches your R output.
2. Enter positive evidence or likelihood values when using ratios.
3. Enter prior and posterior probability when using the odds method.
4. Enter BIC values when using the approximation option.
5. Click Calculate to show results below the header and above the form.
6. Download CSV or PDF to save a report copy.

Article

Understanding Bayes Factors

A Bayes factor compares two hypotheses using the data at hand. It asks how much more likely the observed evidence is under one model than another. The value is usually written as BF10 when the first model is compared with the null model. A value above one supports the first model. A value below one supports the null model.

Why R Users Need This Calculator

R can calculate Bayes factors through packages, custom likelihood functions, or approximations from model information criteria. Those outputs can look different across workflows. This calculator gives a common reporting layer. It accepts direct evidence, likelihood values, posterior odds, or BIC values. It then returns BF10, BF01, log values, posterior probability, and a clear strength label.

Using Evidence Carefully

Bayesian evidence depends on the models, priors, and assumptions. A large factor is not automatic proof. It only says the data were more expected under one model. Priors should match the research question. Model definitions should be stated before comparing results. This is important when using t tests, regression models, or contingency tables in R.

Interpreting the Output

The calculator uses common evidence bands. Values from one to three are weak. Values from three to ten are moderate. Larger values show stronger comparative evidence. The inverse factor, BF01, helps when the null model is favored. Log Bayes factors are useful when values are very large or small.

Reporting Results

A good report includes the method used, the hypotheses, the prior setting, and the final Bayes factor. You can also include posterior odds when a prior probability was supplied. The export tools help save a compact audit trail. The example table shows how the same logic works across different inputs. Always keep raw R output with your analysis files. That makes the result easier to review, reproduce, and explain.

Limits and Checks

Check every denominator before calculation. Zero values make the ratio invalid. Negative evidence values are also not meaningful. For BIC inputs, lower values represent better balance between fit and complexity. The approximation can be helpful for quick work, but exact model comparison is better when available. Review assumptions with your adviser, team, or statistician when findings support important decisions in applied research settings.

FAQs