Abstract
Traditional experimental design techniques have long been employed in industrial, agricultural, and other physical settings to characterize and optimize systems and processes. Such physical systems are characterized by random error, resulting in inconsistent behavior under identical operating conditions. The issues associated with such a random error (or stochastic) component have been addressed in classical design of experiments (DOE), and methods for handling such error are well documented by Myers (2002). In many modern applications, adequate experimentation of physical systems is too costly and/or time consuming, so Fang et al. (2006) suggest that computer simulations are becoming more prominent as computing power increases. Simulations serve as surrogates of physical systems and make use of uncertain or imprecise parameters. Insight about a physical system derived from a simulation should be taken into account with this uncertainty. Sensitivity and uncertainty analyses are tools that support validation and verification and allow an experimenter to place confidence in simulation results. One means to satisfy this end is by conducting and analyzing a computer experiment. A computer experiment is defined by Currin (1988) as a collection of runs from a simulation in which a record of response variables are logged and examined.
Many computer simulations are deterministic, that is identical operating conditions produce no variability in system performance. This poses a problem for traditional statistical modeling methods that are related to DOE, as these classical methods assume that the errors are independently and identically distributed. Models derived from ordinary least squares (OLS) regression assume that variance is fixed over the design space. However, Fang et al. (2006) mention that a deterministic simulation does not have constant variance, as observed points in the design space are precisely known. Because usual uncertainty measurements derived from OLS residuals are not sensible in this case, Currin (1988), Denison et al. (2002), Fang et al. (2006), and Sacks (1989) suggest that a Bayesian approach to regression modeling is more appropriate than traditional techniques because traditional, non-Bayesian approaches fail to take uncertainty of the parameters into account. Bayesian methods involve optimization over the unknown parameters and allow the modeler to make prior assumptions on the regression variance and therefore may be better suited for predicting unobserved responses. The following study compares traditional methods to other techniques including Bayesian regression.
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