Generalized

likelihood The likelihood function (often simply called the likelihood) represents the probability of random variable realizations conditional on particular values of the statistical parameters. Thus, when evaluated on a given sample, the likelihood functi ...

uncertainty Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable ...

estimation Estimation (or estimating) is the process of finding an estimate or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. The value is nonetheless usable because it is de ...

(GLUE) is a statistical method used in

hydrology Hydrology () is the scientific study of the movement, distribution, and management of water on Earth and other planets, including the water cycle, water resources, and environmental watershed sustainability. A practitioner of hydrology is call ...

for quantifying the uncertainty of model predictions. The method was introduced by Keith Beven and Andrew Binley in 1992. The basic idea of GLUE is that given our inability to represent exactly in a

mathematical model A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...

how nature works, there will always be several different models that mimic equally well an observed natural process (such as river discharge). Such equally acceptable or

behavioral Behavior (American English) or behaviour (British English) is the range of actions and mannerisms made by individuals, organisms, systems or artificial entities in some environment. These systems can include other systems or organisms as we ...

models are therefore called equifinal. The methodology deals with models whose results are expressed as

probability distribution In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon ...

s of possible outcomes, often in the form of

Monte Carlo simulation Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be determi ...

s, and the problem can be viewed as assessing, and comparing between models, how good these representations of uncertainty are. There is an implicit understanding that the models being used are approximations to what might be obtained from a thorough

Bayesian analysis Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and e ...

of the problem if a fully adequate model of real-world hydrological processes were available.Beven, K.J., 2007
Towards integrated environmental models of everywhere: uncertainty, data and modelling as a learning process.

Hydrology and Earth System Sciences ''Hydrology and Earth System Sciences'' (HESS) is a monthly peer reviewed open access scientific journal that publishes original research in hydrology and related field like water resource management. The journal is published by Copernicus Pu ...

, 11(1), p. 460–467. GLUE is equivalent to

Approximate Bayesian computation Approximate Bayesian computation (ABC) constitutes a class of computational methods rooted in Bayesian statistics that can be used to estimate the posterior distributions of model parameters. In all model-based statistical inference, the like ...

for some choices of summary statistic and threshold

References

Hydrology Probability assessment Bayesian statistics {{hydrology-stub