Noninformative

Noninformative is a term used in statistics to describe priors or data summaries that aim to convey little or no information about a parameter. In Bayesian analysis, a noninformative (or uninformative) prior is chosen to let the data drive the posterior distribution when prior knowledge is poor or unavailable. The goal is to minimize prior influence, though no prior can be truly ignorant across all questions.

Common approaches include flat (uniform) priors, which assign equal weight to all values over a specified range. Flat priors can be informative through the chosen parameterization or bounds, and in some cases are improper (do not integrate to a finite total mass). Another approach is the Jeffreys prior, derived from the Fisher information and invariant under reparameterization; it often takes the form of scale priors such as proportional to 1/θ for scale parameters. More formal settings use reference or default priors (e.g., Bernardo–Berger reference priors) constructed to maximize information about a target quantity.

Noninformative priors are used in problems ranging from estimating a mean with known variance to more complex models with multiple parameters, where joint priors attempt to remain as noncommittal as possible. They are also relevant in model selection and hierarchical modeling, where the aim is to avoid overpowering the data with subjective beliefs.

Critiques emphasize that no prior is universally noninformative; results may depend on parameterization, model assumptions, or data quality. Improper priors risk yielding undefined posteriors, and sensitivity analyses are recommended to assess robustness. In practice, researchers select priors to reflect genuine ignorance or to achieve invariance properties desirable for the problem at hand.