ABSTRACT
In the study of complex physical and engineering processes, it is sometimes impossible, infeasible, or very expensive to observe the actual systems. Examples of such processes include climate change, spread of infectious diseases, and car crashes-(see Jones et al. 1998 and Santner et al. 2003). In such situations, we can sometimes use computer codes (simulators) tomimic the process that we desire to investigate. Values of the input variables are supplied to the computer code, and the code produces the corresponding values of the output variable. To study the nature of the relationship between the input variables and the output variable, it would be ideal if we could observe the code output for all possible values of the input variables. Often, however, the computer code itself is very complex and each run of the simulator turns out to be highly expensive or very time-consuming. This limits the number of times we can run the simulator. In what follows, we assume the computer code runs slowly and that the number of times we can observe the simulator is “small.”
