Stochastic Process Models for Describing Computer Simulator Output

  • Thomas J. Santner
  • Brian J. Williams
  • William I. Notz
Part of the Springer Series in Statistics book series (SSS)


Recall from Chap.  1 that \(\boldsymbol{x}\) denotes a generic input to our computer simulator and \(y(\boldsymbol{x})\) denotes the associated output. This chapter will introduce several classes of random function models for \(y(\boldsymbol{x})\) that will serve as the core building blocks for the interpolators, experimental designs, calibration, and tuning methodologies that will be introduced in later chapters. The reason that the random function approach is so useful is that accurate prediction based on black box computer simulator output requires a rich class of \(y(\boldsymbol{x})\) options when only a minimal amount might be known about the output function. Indeed, regression mean modeling of simulator output is usually based on a rather arbitrarily selected parametric form.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Thomas J. Santner
    • 1
  • Brian J. Williams
    • 2
  • William I. Notz
    • 1
  1. 1.Department of StatisticsThe Ohio State UniversityColumbusUSA
  2. 2.Statistical Sciences GroupLos Alamos National LaboratoryLos AlamosUSA

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