Metauncertainty

Metauncertainty is the uncertainty about the uncertainty estimates themselves. It describes second-order or higher-order uncertainty: doubt about how reliable, accurate, or well calibrated the quantities used to quantify uncertainty are. In practical terms, metauncertainty concerns whether the models, data, priors, and assumptions behind probabilistic forecasts are appropriate, and how much faith should be placed in the resulting uncertainty intervals or probabilities.

Sources of metauncertainty include model misspecification, incorrect or incomplete prior beliefs, nonstationarity in data,

measurement error, and limited or biased data. Metauncertainty also arises when multiple competing models yield different uncertainty assessments, or when predictive distributions fail to capture real-world variability.

Assessment and management of metauncertainty often involve conceptually second-order methods. Techniques include calibration and validation of probabilistic forecasts, posterior predictive checks, sensitivity analyses, and ensemble or model-averaging approaches to reflect model disagreement. Robust decision making, scenario analysis, and distribution-free methods can help mitigate reliance on any single uncertain quantification. In Bayesian contexts, hierarchical modeling and explicit modeling of prior uncertainty can propagate higher-order uncertainty through to inferences and decisions.

Metauncertainty is especially relevant in fields relying on probabilistic forecasts under uncertainty, such as climate science, finance, epidemiology, and artificial intelligence. Recognizing metauncertainty encourages cautious interpretation of uncertainty estimates and supports strategies that remain reliable across plausible variations in how uncertainty is quantified.