Weakly informative prior

by W. B. Meitei, PhD

A weakly informative prior in Bayesian statistics is a type of prior distribution that provides some guidance to the analysis by incorporating modest, reasonable information about the parameters but does not impose overly strong assumptions. Its purpose is to regularise the model, constraining estimates within a plausible range to prevent extreme or nonsensical values, while still allowing data to influence the posterior inference substantially.

Unlike noninformative priors that aim to contribute almost no information (and can lead to unstable or unrealistic estimates), weakly informative priors strike a balance by:

• Steering estimates away from implausible extremes.
• Improving stability, especially when data are sparse or noisy,
• Avoiding overfitting through gentle shrinkage towards reasonable values.

For example, a weakly informative prior on a regression coefficient might be a normal distribution centred at zero with a moderately large standard deviation (e.g., Normal (0, 5²)), which allows the coefficient to vary widely but discourages implausibly large effects.

Using weakly informative priors helps make Bayesian analyses more robust and interpretable, reducing risks of misleading results due to overly vague or improper priors, while still respecting the data's signal.

Suggested Readings:

1. Gelman, A., Jakulin, A., Pittau, M. G., & Su, Y. S. (2008). A weakly informative default prior distribution for logistic and other regression models.
2. Evans, M., & Jang, G. H. (2011). Weak informativity and the information in one prior relative to another. Statistical Science. 26(3), 423-439.
3. Hamra, G. B., MacLehose, R. F., & Cole, S. R. (2013). Sensitivity analyses for sparse-data problems—using weakly informative Bayesian priors. Epidemiology, 24(2), 233-239.
4. Lemoine, N. P. (2019). Moving beyond noninformative priors: why and how to choose weakly informative priors in Bayesian analyses. Oikos, 128(7), 912-928.
5. Weakly informative (uninformed) priors. EPIX Analytics.

Suggested Citation: Meitei, W. B. (2025). Weakly informative prior. WBM STATS.