Computer simulations are constructed to emulate a physical system.
Because these are meant to replicate some aspect of a system in detail, they often do not yield an analytic solution.
Therefore, methods such as discrete event simulation or finite element solvers are used.
For example, climate models are often used because experimentation on an earth sized object is impossible.
Some of those include: Modeling of computer experiments typically uses a Bayesian framework.
In the realm of computer experiments, the Bayesian interpretation would imply we must form a prior distribution that represents our prior belief on the structure of the computer model.
The use of this philosophy for computer experiments started in the 1980s and is nicely summarized by Sacks et al. (1989) [1].
The basic idea of this framework is to model the computer simulation as an unknown function of a set of inputs.
Examples of inputs to these simulations are coefficients in the underlying model, initial conditions and forcing functions.
It is natural to see the simulation as a deterministic function that maps these inputs into a collection of outputs.
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, evaluation of the output for a single set of inputs can require millions of computer hours [3].
The typical model for a computer code output is a Gaussian process.
Since a Gaussian process prior has an infinite dimensional representation, the concepts of A and D criteria (see Optimal design), which focus on reducing the error in the parameters, cannot be used.
Popular strategies for design include latin hypercube sampling and low discrepancy sequences.
Matrix inversion of large, dense matrices can also cause numerical inaccuracies.
Currently, this problem is solved by greedy decision tree techniques, allowing effective computations for unlimited dimensionality and sample size patent WO2013055257A1, or avoided by using approximation methods, e.g. [6].