Calculator inputs
Example data table
| Model | Posterior Mean Deviance D̄ | D(θ̄) | pD | DIC | Rank |
|---|---|---|---|---|---|
| Model A | 121.4000 | 116.8000 | 4.6000 | 126.0000 | 1 |
| Model B | 124.9000 | 118.7000 | 6.2000 | 131.1000 | 2 |
| Model C | 126.1000 | 117.0000 | 9.1000 | 135.2000 | 3 |
Lower DIC values generally indicate a preferred model when all models are fit to the same data with the same likelihood structure.
Formula used
The calculator uses the standard deviance information criterion framework for Bayesian model comparison.
Posterior mean deviance: D̄ = average posterior deviance
Effective number of parameters: pD = D̄ − D(θ̄)
Deviance Information Criterion: DIC = D̄ + pD = 2D̄ − D(θ̄)
Where:
- D̄ is the posterior average of deviance values.
- D(θ̄) is the deviance evaluated at posterior mean parameters.
- pD estimates effective model complexity.
- DIC balances fit and complexity, where lower is better.
How to use this calculator
- Select the calculation method that matches your available Bayesian output.
- Enter either D̄ and D(θ̄), D̄ and pD, or posterior deviance samples with D(θ̄).
- Optionally enter another model’s DIC for direct comparison.
- Press Calculate DIC to show the result below the header and above the form.
- Review DIC, pD, complexity notes, and the comparison summary.
- Use the CSV or PDF buttons to export your result.
Frequently asked questions
1. What does DIC measure?
DIC measures Bayesian model adequacy by combining goodness of fit with a penalty for effective model complexity. It helps compare models fitted to the same dataset.
2. Is a lower DIC always better?
Lower DIC is preferred when the compared models use the same response data, likelihood structure, and outcome definition. It should not be compared across unrelated datasets.
3. What is pD in this calculator?
pD is the effective number of parameters. It reflects model flexibility rather than raw parameter count and helps show how much complexity contributes to the final criterion.
4. Why can pD become negative?
Negative pD can appear with unstable posterior summaries, multimodal posteriors, or weak regularity conditions. It is a warning sign that DIC may need careful interpretation.
5. Can I use posterior samples directly?
Yes. Choose the sample method, paste posterior deviance values, and enter D(θ̄). The calculator computes D̄, pD, DIC, and basic sample summary statistics.
6. What DIC difference is meaningful?
Small differences below 2 often suggest little practical separation. Differences above 5 usually indicate stronger evidence for the model with lower DIC.
7. How is DIC different from AIC or BIC?
DIC is designed for Bayesian models and uses posterior-based complexity. AIC and BIC are more common in classical likelihood settings and use different penalty structures.
8. Can I export my results?
Yes. After calculation, you can export the displayed result as a CSV file or a PDF summary for documentation, reporting, or model review workflows.