PlausibilityFunktionen

PlausibilityFunktionen, or plausibility functions, are a formal tool in statistical inference that assign to each parameter value θ a degree of plausibility given the observed data y. They produce a map pl_y: Θ → [0,1], intended to summarize the evidential support for competing parameter values without relying on prior probabilities.

The construction relies on a statistical model for the data and a predictive mechanism, such as a predictive random set, to translate sampling variability into a plausibility measure. For a subset A of the parameter space, the plausibility pl_y(A) reflects how compatible A is with the observed data; larger values indicate greater compatibility. Plausibility regions are sets of θ with pl_y({θ}) above a chosen threshold and function much like confidence regions without relying on priors.

Properties of plausibility functions include the ability to yield calibrated uncertainty statements under correct model specification, offering either exact or approximate coverage for plausibility-based regions. They are typically prior-free, distinguishing them from Bayesian posteriors, and provide a distribution-free interpretation in compatible settings.

Relation to other methods: plausibility functions relate to p-values and confidence intervals but offer a unified, single-valued measure of plausibility for parameter values or subsets. This makes them applicable to hypothesis testing, interval estimation, and model checking within the same framework.

Applications and limitations: They are used in small-sample settings and in robust inference where priors are undesirable. Computationally, construction often requires simulation or optimization, and results depend on the chosen predictive mechanism and on potential model misspecification.

See also: p-value, confidence distribution, inferential models.