Many scientific phenomena are now investigated by complex computer models or codes A computer experiment is a number of runs of the code with various inputs A feature of many computer experiments is that the output is deterministic--rerunning the code with the same inputs gives identical observations Often, the codes are computationally expensive to run, and a common objective of an experiment is to fit a cheaper predictor of the output to the data Our approach is to model the deterministic output as the realization of a stochastic process, thereby providing a statistical basis for designing experiments (choosing the inputs) for efficient prediction With this model, estimates of uncertainty of predictions are also available Recent work in this area is reviewed, a number of applications are discussed, and we demonstrate our methodology with an example

/pdf/the-design-and-analysis-of-computer-experiments-1kfo89lyf2.pdf

The design and analysis of computer experiments

We consider prediction and uncertainty analysis for systems which are approximated using complex mathematical models. Such models, implemented as computer codes, are often generic in the sense that by a suitable choice of some of the model's input parameters the code can be used to predict the behaviour of the system in a variety of specific applications. However, in any specific application the values of necessary parameters may be unknown. In this case, physical observations of the system in the specific context are used to learn about the unknown parameters. The process of fitting the model to the observed data by adjusting the parameters is known as calibration. Calibration is typically effected by ad hoc fitting, and after calibration the model is used, with the fitted input values, to predict the future behaviour of the system. We present a Bayesian calibration technique which improves on this traditional approach in two respects. First, the predictions allow for all sources of uncertainty, including the remaining uncertainty over the fitted parameters. Second, they attempt to correct for any inadequacy of the model which is revealed by a discrepancy between the observed data and the model predictions from even the best-fitting parameter values. The method is illustrated by using data from a nuclear radiation release at Tomsk, and from a more complex simulated nuclear accident exercise.

https://www.jstor.org/stable/pdfplus/2680584.pdf

Bayesian Calibration of computer models

A computational model is a representation of some physical or other system of interest, first expressed mathematically and then implemented in the form of a computer program; it may be viewed as a function of inputs that, when evaluated, produces outputs. Motivation for this article comes from computational models that are deterministic, complicated enough to make classical mathematical analysis impractical and that have a moderate-to-large number of inputs. The problem of designing computational experiments to determine which inputs have important effects on an output is considered. The proposed experimental plans are composed of individually randomized one-factor-at-a-time designs, and data analysis is based on the resulting random sample of observed elementary effects, those changes in an output due solely to changes in a particular input. Advantages of this approach include a lack of reliance on assumptions of relative sparsity of important inputs, monotonicity of outputs with respect to inputs, or ad...

Factorial sampling plans for preliminary computational experiments

The design and analysis of computer experiments as a relatively young research field is not only of high importance for many industrial areas but also presents new challenges and open questions for statisticians. This editorial introduces a special issue devoted to the topic. The included papers present an interesting mixture of recent developments in the field as they cover fundamental research on the design of experiments, models and analysis methods as well as more applied research connected to real-life applications.

/pdf/design-and-analysis-of-computer-experiments-2qj5hjkiha.pdf

Design and analysis of computer experiments

In structural optimization, usually an approximation concept is introduced as interface between (FEM) structural analysis code and optimization algorithm. In some cases of optimm desigr., a glcba! apprcxhaticl? ccncept car. be effectively applied. Then, apprmirnatior. model functions are built of all objective and constraint functions, whose values, for a certain design point, follow from the structural analysis calculations. In this way, the original o p timization problem is completely replaced by an explicitly known approximate optimization problem. Response-surface techniques are commonly applied to build global approximation models, especially when dealing with responses of physical experiments. For one response function, this means that a user defined model function is fitted to the response data calculated at the design sites of some experimental design. Errors between model function and experimental response values are assumed to be randomly distributed. However, in the structural optimization case, an experiment is a computer analysis with a deterministic response as a result. This rules out the statistical assumptions response-surface model building is based upon. Furthermore, it is often difficult to find model functions that approximate the true response behaviour within the desired accuracy. Sacks and coworkers proposed a new model building strategy, that is especially suited for deterministic computer responses. Their basic assumption is that computer responses can be modelled as a realization of a stochastic process. This finally leads to a response prediction that exactly describes all calculated computer responses. Additionally, the mean squared error of a prediction can be calculated, which serves as a measure of accuracy of the prediction. A review is given of the method of Sacks et al.. It has been implemented in MATLAB. Some analytical response functions and small design optimization problems have been used to test the model building capacities and the effectiveness of the method when applied as global approximation concept in structural optimization. It is concluded that the strategy as proposed by Sacks and coworkers is not suited for implementation in a design optimization tool, mainly because of two reasons. Firstly, maximum likelihood parameter estimation is computationally expensive and not straightforward, while the quality of the parameter estimations is questionable. This computational effort is disadvantageous if many constraint functions have to approximated, which often occurs in structural optimization. Secondly, the mean squared error can not be unconditionally trusted. To have an independent accuracy measure several additional computer experiments (test points) have to be performed. Main advantage of the approximations of Sacks et al., compared with response-surface models, is the flexibility to automatica!!y adapt to the ca!cu!ated response data. The same sort, of flexibility also occurs for the moving least-squares variant of the least-squares parameter estimation. I t is recommended to investigate whether this method can add flexibility to, and solve the model function selection problems of, the response-surface strategy without an unmanageable amount of computations.

/pdf/design-and-analysis-of-computer-experiments-2ytzwoggmf.pdf

Design and Analysis of Computer Experiments

A computer experiment generates observations by running a computer model at inputs x and recording the output (response) Y. Prediction of the response Y to an untried input is treated by modeling the systematic departure of Y from a linear model as a realization of a stochastic process. For given data (selected inputs and the computed responses), best linear prediction is used. The design problem is to select the inputs to predict efficiently. The issues of choice of stochastic-process model and computation of efficient designs are addressed, and applications are made to some chemical kinetics problems.

Designs for Computer Experiments

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Designs for Computer Experiments