The following glossary explains some of the central UQ concepts using quotes from the seminal paper
Kennedy and Ohagan 2001 “Bayesian calibration of computer models”
“Crudely put, calibration is the activity of adjusting the unknown […] parameters until the outputs of the model fit the observed data.”
“More generally, a computer model will have a number of context-specific inputs that define a particular situation in which the model is to be used. When, as is often the case, the values of one or more of the context-specific inputs are unknown, observations are used to learn about them. This is calibration. In current practice, calibration invariably consists of searching for a set of values of the unknown inputs such that the observed data fit as closely as possible, in some sense, to the corresponding outputs of the model. These values are considered as estimates of the context- specific inputs, and the model is then used to predict the behaviour of the process in this context by setting these inputs to their estimates. Clearly, this ‘plug-in’ prediction treats the context-specific inputs as if they were known. The reality is that they are only estimated, and residual uncertainty about these inputs should be recognized in subsequent predictions from the model.”
“No model is perfect. Even if there is no parameter uncertainty […] the predicted value will not equal the true value of the process. The discrepancy is model inadequacy. Since the real process may itself exhibit random variability, we define model inadequacy to be the difference between the true mean value of the real world process and the code output at the true values of the inputs. […] Given that there is model inadequacy, we cannot think of the true input values as those which lead to perfect predictions being outputted, so how can we define true values for the uncertain input parameters?”
“[…] it is not realistic to say that the [computer model] output is known for given inputs before we actually run the code and see that output. It may not be practical to run the code to observe the output for every input configuration of interest, in which case uncertainty about code output needs to be acknowledged.”
“[…] given data comprising outputs at a sample of input configurations, the problem is to estimate the output at some other input configuration for which the code has not yet been run. This is relevant when the code is particularly large and expensive to run. […] The only form of uncertainty accounted for [by interpolation] is code uncertainty.”
“The objective of uncertainty analysis is to study the distribution of the code output that is induced by probability distributions on inputs. […] The simplest approach to uncertainty analysis is a Monte Carlo solution in which configurations of inputs are drawn at random from their distribution. The code is then run for each sample input configuration and the resulting set of outputs is a random sample from the output distribution […]. The Monte Carlo method for uncertainty analysis is simple but becomes impractical when the code is costly to run, because of the large number of runs required. More efficiency is claimed for Latin hypercube sampling.”
“[…] whose goal is to characterize how the code output responds to changes in the inputs, with particular reference to identifying inputs to which the output is relatively sensitive or insensitive. […] As with interpolation, these statistical approaches to sensitivity analysis only take account of […] code uncertainty.”