Design and Analysis of Computer Experiments

1 Introduction

In many scientific and application areas, physical experimentations can be intensive or very difficult in terms of material, time, and cost. For example, it is almost impossible to conduct experimentation on an earth sized object for the weather forecast. The advance of modern computers and computer-aided design methodologies have given rise to a more economical mode of experimentation called computer experiments. Computer experiments are executed on computers using physical models and numerical methods such as finite-element-based methods and agent-based methods. Due to the complexity and inherent nature of computer models, design and analysis of computer models are quite different from the traditional de- sign and analysis of physical experiments. Computer experiments usually involve complex systems with a large number of input variables (Schmidt, Cruz, & Iyengar, 2005). Moreover, computer experiments are often deterministic. It means that replicate observations from executing the computer code with the same inputs will be identical. Thus, the conventional design and analysis of physical experiments would not be appropriate for design and analysis of computer experiments. Because of the deterministic nature of computer experiments, the modeling and analysis of computer experiments will concern more on the bias but not on reducing variance. The de- sign and analysis of computer experiments has received wide attentions in the past decades (Santner, Williams, & Notz, 2003; Fang & Sudjianto, 2006; Sacks, Welch, Mitchell, & Wynn, 1989). The uncertainty quantification and cali- bration of computer experiments also have attracted wide attentions (Kennedy & O’Hagan, 2000; Oakley & O’Hagan, 2002; Higdon, Gattiker, Williams, & Rightley, 2008).

The discussions in this chapter focus on the statistical design and analysis of computer experiments. Existing statistical designs for conducting computer experiments are reviewed in Section 3.2.1. A recent development of statistical designs is introduced in Section 3.2.2 which takes into account a commonly occurred situation where both quantitative and qual- itative variables are involved. Based on the outputs of computer simulations, statistical emulators can be built. Modeling and analysis techniques for building such emulators are reviewed in Section 3.3. Conclusions and remarks are provided in Section 3.4.