# A Bayesian Approach to the Design and Analysis of Computer Experiments

## Abstract

We consider the problem of designing and analyzing experiments for prediction of the function y(f), t {element_of} T, where y is evaluated by means of a computer code (typically by solving complicated equations that model a physical system), and T represents the domain of inputs to the code. We use a Bayesian approach, in which uncertainty about y is represented by a spatial stochastic process (random function); here we restrict attention to stationary Gaussian processes. The posterior mean function can be used as an interpolating function, with uncertainties given by the posterior standard deviations. Instead of completely specifying the prior process, we consider several families of priors, and suggest some cross-validational methods for choosing one that performs relatively well on the function at hand. As a design criterion, we use the expected reduction in the entropy of the random vector y (T*), where T* {contained_in} T is a given finite set of ''sites'' (input configurations) at which predictions are to be made. We describe an exchange algorithm for constructing designs that are optimal with respect to this criterion. To demonstrate the use of these design and analysis methods, several examples are given, including one experiment on a computer model ofmore »

- Authors:

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- US Department of Energy (US)

- OSTI Identifier:
- 814584

- Report Number(s):
- ORNL-6498

TRN: US200318%%70

- DOE Contract Number:
- AC05-00OR22725

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 1 Jan 1988

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; COMPUTER CODES; COMPUTERS; DESIGN; ENERGY STORAGE; ENTROPY; FORECASTING; GAUSSIAN PROCESSES; INTEGRATED CIRCUITS; VECTORS

### Citation Formats

```
Currin, C.
```*A Bayesian Approach to the Design and Analysis of Computer Experiments*. United States: N. p., 1988.
Web. doi:10.2172/814584.

```
Currin, C.
```*A Bayesian Approach to the Design and Analysis of Computer Experiments*. United States. https://doi.org/10.2172/814584

```
Currin, C. 1988.
"A Bayesian Approach to the Design and Analysis of Computer Experiments". United States. https://doi.org/10.2172/814584. https://www.osti.gov/servlets/purl/814584.
```

```
@article{osti_814584,
```

title = {A Bayesian Approach to the Design and Analysis of Computer Experiments},

author = {Currin, C},

abstractNote = {We consider the problem of designing and analyzing experiments for prediction of the function y(f), t {element_of} T, where y is evaluated by means of a computer code (typically by solving complicated equations that model a physical system), and T represents the domain of inputs to the code. We use a Bayesian approach, in which uncertainty about y is represented by a spatial stochastic process (random function); here we restrict attention to stationary Gaussian processes. The posterior mean function can be used as an interpolating function, with uncertainties given by the posterior standard deviations. Instead of completely specifying the prior process, we consider several families of priors, and suggest some cross-validational methods for choosing one that performs relatively well on the function at hand. As a design criterion, we use the expected reduction in the entropy of the random vector y (T*), where T* {contained_in} T is a given finite set of ''sites'' (input configurations) at which predictions are to be made. We describe an exchange algorithm for constructing designs that are optimal with respect to this criterion. To demonstrate the use of these design and analysis methods, several examples are given, including one experiment on a computer model of a thermal energy storage device and another on an integrated circuit simulator.},

doi = {10.2172/814584},

url = {https://www.osti.gov/biblio/814584},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1988},

month = {1}

}