Uncertainty quantification

Uncertainty quantification is the use of mathematical and computational methods to describe, propagate, and analyze uncertainty in data, parameters, and model outputs.

Probability distribution: A mathematical description of the possible values of a random variable and their probabilities. Distributions encode uncertain inputs and outputs in probabilistic analyses.
Random variable: A variable whose possible values are associated with a probability distribution. It provides the basic representation of uncertain quantities.
Weather forecasting: The use of observations and models to predict the future state of the atmosphere. Ensemble forecasts communicate uncertainty in possible atmospheric outcomes.
Fuzzy logic: A logic in which truth can take graded values between fully false and fully true. It represents vagueness through graded membership, not probability of outcomes.
Model uncertainty: Uncertainty arising from the choice, structure, or assumptions of a model. Accounting for alternative model structures remains difficult when they produce different predictions.
Bayesian inference: A framework for updating probability distributions over hypotheses or parameters using observed evidence. It combines prior knowledge with data to quantify parameter uncertainty.
Aleatoric uncertainty: Uncertainty arising from inherent variability in a process or measurement. It captures variation that remains even with perfect knowledge of model parameters.
Climate modeling: The simulation of climate processes and their interactions to study past, present, or future climate. Uncertainty analysis separates sources of spread in long-term projections.
Dempster–Shafer theory: A framework that assigns belief to sets of hypotheses when evidence does not support precise probabilities. It permits imprecise evidence assignments beyond ordinary probability distributions.
Distribution shift: A change between the data distribution used to develop a model and the distribution encountered in use. Uncertainty estimates may fail when deployment data differ from calibration data.

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