Priorien

Priorien is a term used in theoretical discussions and some speculative fiction to denote a meta-prior—a probability distribution over prior distributions in Bayesian reasoning. The term is not a standard concept in formal statistics, but it is employed to explore how uncertainty about the priors themselves can affect inference. It serves as a way to discuss robustness to prior choices and to highlight the role of meta-uncertainty in modeling.

Etymology and scope: The word combines the notion of a prior with the suffix -ien, forming a noun for a class of ideas rather than a single prior. In practice, priorien is invoked to imagine a distribution over priors, rather than a single fixed prior, and to consider how conclusions might change when priors are themselves uncertain.

Concept and formalism: A priorien is a distribution over priors. If p(theta) is a prior for a parameter theta and P* is a distribution over possible priors (or over hyperparameters that define priors), then one can conceptually average inferences across priors drawn from P*. This leads to a higher-order approach related to hierarchical modeling and hyperpriors, capturing meta-uncertainty about the inference process itself.

Applications and reception: Priorien is mainly used in thought experiments, pedagogical discussions, and some fictional settings to illustrate how conclusions depend on assumptions about priors. In formal statistics, practitioners typically prefer explicit hierarchical models or robust priors and, when possible, sensitivity analyses, rather than adopting a fully specified priorien.

See also: Bayesian inference, hierarchical modeling, hyperprior, prior, model misspecification, robustness.