Computer experiment: Difference between revisions

Revision as of 11:52, 25 April 2014

Revision as of 11:54, 25 April 2014

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[[Computer simulation]]s 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. A [[computer model]] is used to make inferences about the system it replicates. For example, [[climate models]] are often used because experimentation on an earth sized object is impossible.

==Objectives==

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Computer experiments have been employed with many purposes in mind. Some of those include:

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* [[Uncertainty quantification]]: Characterize the uncertainty present in a computer simulation arising from unknowns during the computer simulation's construction.

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* [[Inverse problem]]s: Discover the underlying properties of the system from the physical data.

* '''Bias correction''': Use physical data to correct for bias in the simulation.

* [[Data assimilation]]: Combine multiple simulations and physical data sources into a complete predictive model.

* [[Systems design]]: Find inputs that result in optimal system performance measures.

==Computer simulation modeling==

Modeling of computer experiments typically uses a Bayesian framework. [[Bayesian statistics]] is an interpretation of the field of [[statistics]] where which all evidence about the true state of the world is explicitly expressed in the form of [[probabilities]]. 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) [http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.ss/1177012413]. While the Bayesian approach is widely used, [[frequentist]] approaches have been recently discussed [http://www2.isye.gatech.edu/~jeffwu/publications/calibration-may1.pdf].

"PETER PAN "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, evaluatution of the output for a single set of inputs can require millions of computer hours [http://amstat.tandfonline.com/doi/abs/10.1198/TECH.2009.0015#.UbixC_nFWHQ].