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The Design and Analysis of Computer Experiments pp 27–66Cite as

Stochastic Process Models for Describing Computer Simulator Output

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Abstract

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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Authors and Affiliations

  1. Department of Statistics, The Ohio State University, Columbus, OH, USA

    Thomas J. Santner & William I. Notz

  2. Statistical Sciences Group, Los Alamos National Laboratory, Los Alamos, NM, USA

    Brian J. Williams

Authors
  1. Thomas J. Santner
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  2. Brian J. Williams
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  3. William I. Notz
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Santner, T.J., Williams, B.J., Notz, W.I. (2018). Stochastic Process Models for Describing Computer Simulator Output. In: The Design and Analysis of Computer Experiments. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-8847-1_2

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