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The basic idea of this framework is to model the computer simulation as an unknown function of a set of inputs. The computer simulation is implemented as a piece of computer code that can be evaluated to produce a collection of outputs. Examples of inputs to these simulations are coefficients in the underlying model, [[initial conditions]] and [[Forcing function (differential equations)|forcing functions]]. It is natural to see the simulation as a deterministic function that maps these ''inputs'' into a collection of ''outputs''. On the basis of seeing our simulator this way, it is common to refer to the collection of inputs as <math>x</math>, the computer simulation itself as <math>f</math>, and the resulting output as <math>f(x)</math>. Both <math>x</math> and <math>f(x)</math> are vector quantities, and they can be very large collections of values, often indexed by space, or by time, or by both space and time.
Although <math>f(\cdot)</math> is known in principle, in practice this is not the case. Many simulators comprise tens of thousands of lines of high-level computer code, which is not accessible to intuition. For some simulations, such as climate models,
===Gaussian process prior===
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