The Annals of Applied Statistics

Parallel partial Gaussian process emulation for computer models with massive output

Mengyang Gu and James O. Berger

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We consider the problem of emulating (approximating) computer models (simulators) that produce massive output. The specific simulator we study is a computer model of volcanic pyroclastic flow, a single run of which produces up to $10^{9}$ outputs over a space–time grid of coordinates. An emulator (essentially a statistical model of the simulator—we use a Gaussian Process) that is computationally suitable for such massive output is developed and studied from practical and theoretical perspectives. On the practical side, the emulator does unexpectedly well in predicting what the simulator would produce, even better than much more flexible and computationally intensive alternatives. This allows the attainment of the scientific goal of this work, accurate assessment of the hazards from pyroclastic flows over wide spatial domains. Theoretical results are also developed that provide insight into the unexpected success of the massive emulator. Generalizations of the emulator are introduced that allow for a nugget, which is useful for the application to hazard assessment.

Article information

Ann. Appl. Stat., Volume 10, Number 3 (2016), 1317-1347.

Received: January 2015
Revised: April 2016
First available in Project Euclid: 28 September 2016

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Zentralblatt MATH identifier

Gaussian process computer model emulation space–time coordinate objective Bayesian analysis


Gu, Mengyang; Berger, James O. Parallel partial Gaussian process emulation for computer models with massive output. Ann. Appl. Stat. 10 (2016), no. 3, 1317--1347. doi:10.1214/16-AOAS934.

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Supplemental materials

  • Supplement to “Parallel partial Gaussian process emulation for computer models with massive output”. This supplement consists of three parts. The first part describes the “periodic folding” method for modeling the correlation between periodic inputs. The second part provides some numerical results that the PP GaSP emulator with a nugget is close to being an interpolator for the TITAN2D computer model. Part 3 discusses a prior for smoothing the draws of the PP GaSP emulator through block sampling.