Generalized

likelihood A likelihood function (often simply called the likelihood) measures how well a statistical model explains observed data by calculating the probability of seeing that data under different parameter values of the model. It is constructed from the j ...

uncertainty Uncertainty or incertitude refers to situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown, and is particularly relevant for decision ...

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 d ...

(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 drainage basin sustainability. A practitioner of hydrology is called a hydro ...

for quantifying the uncertainty of model predictions. The method was introduced by

Keith Beven Keith John Beven (born 23 July 1950) is a British hydrologist and distinguished emeritus professor in hydrology at Lancaster University. According to Lancaster University he is the most highly cited hydrologist. In 2017, Beven was elected a me ...

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 an abstract and concrete, abstract description of a concrete system using mathematics, mathematical concepts and language of mathematics, language. The process of developing a mathematical model is termed ''mathematical m ...

how nature works, there will always be several different models that mimic equally well an observed natural process (such as

river discharge In hydrology, discharge is the volumetric flow rate (volume per time, in units of m3/h or ft3/h) of a stream. It equals the product of average flow velocity (with dimension of length per time, in m/h or ft/h) and the cross-sectional area (in m2 o ...

). Such equally acceptable or

behavioral Behavior (American English) or behaviour (British English) is the range of actions of individuals, organisms, systems or artificial entities in some environment. These systems can include other systems or organisms as well as the inanimate p ...

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 a Function (mathematics), function that gives the probabilities of occurrence of possible events for an Experiment (probability theory), experiment. It is a mathematical descri ...

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 det ...

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 Thomas Bayes ( ; c. 1701 – 1761) was an English statistician, philosopher, and Presbyterian Presbyterianism is a historically Reformed Protestant tradition named for its form of church government by representative assemblies of elde ...

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 () is the scientific study of the movement, distribution, and management of water on Earth and other planets, including the water cycle, water resources, and drainage basin sustainability. A practitioner of hydrology is called a hydro ...

, 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 likel ...

for some choices of summary statistic and threshold.

References

Hydrology Probability assessment Bayesian statistics {{hydrology-stub